The sprawling Castle Hill district, a UNESCO World Heritage site on the Buda side of the Danube is where modern Budapest history begins. The three towns of Buda, Pest and northern Óbuda were joined in 1873 to create the city, but the fortification of Castle Hill began in the 1240s, and served as the seat for Hungary’s kings until the Turkish invasion in 1541. Buda was reborn under the rule of the Austro-Hungarian Empire, when the Hapsburgs (no lovers of subtlety) rebuilt, restored and added to the Royal Palace. During World War II and the infamous siege of Buda, parts of Castle Hill were destroyed, and the Royal Palace burned to the ground.

Much of what you see today has been lovingly and painstakingly reconstructed, but the unembellished exterior of the Hungarian National Gallery (the former Royal Palace) is a sad reminder—and poor imitation—of the palace’s former grandeur. A walk through the Castle Hill district makes it clear that much money has been invested here (a jarring contrast to some of the streets in Pest). The Old Town, with its multicolored buildings and cobblestoned streets, has been polished and prettified, and recalls the Old Town in Prague.

Buda’s Castle Hill comprises several of the city’s most famous sights. The Chain Bridge leads to the funicular (built in 1870, but destroyed during WWII and reopened in 1986) that takes visitors up to the Hungarian National Gallery. Most of the buildings are Gothic or Baroque in style, but some parts date from the 14th century. North of the Royal Palace compound lies the neighborhood of Fisherman’s Bastion, a delicate white stone structure of twisting spires, slender towers and wide staircases that resembles the Ivory Tower in The Neverending Story. Nearby, the Neo-Gothic Matthias Church, with its multicolored-tile roof, rises, and farther north you come into the Old Town.

Indagare Tip: Castle Hill is a sprawl, and if you’re touring on foot, it will take you a day to see everything. For a family-friendly and more compact way of touring the site, Indagare members can contact the Bookings Team to arrange a biking or horse-drawn carriage tour.

When the German Army retreated during World War II, they blew up the seven bridges that connected Pest and Buda to slow down the approaching Russian Army (incidentally, that winter was so cold that the Danube froze, and the soldiers simply marched across the ice). But the pillars of Budapest’s oldest bridge, Széchenyi Lánchíd, survived, and today the elegant structure, with two massive arches framed by stone lions, is a popular landmark. (the bridge was originally commissioned by Count István Széchenyi in 1839, after he was forced to delay his father’s funeral for a week when he was unable to cross the Danube during bad weather. The Four Seasons Gresham Palace has perfect views of it.

Indagare Tip: Indagare members can contact the Bookings Team to arrange a tour of the inner passageways of the bridge, a sure hit with families.

The sprawling park behind Heroes’ Square is a huge green expanse full of numerous discoveries, especially for those traveling with children. It houses the Budapest Zoo, Vidam Park (an old-fashioned amusement park with rickety-looking rides), the Széchenyi bath complex and the fantastical Vajdahunyad Castle, which was built for the Millennium Celebration in 1896 and showcases a bewildering array of architectural styles. There are lawns perfect for picnicking and a large lake where you can wakeboard and boat around in summer, and ice-skate in winter. The acclaimed Gundel restaurant is also in the park.

Europe’s largest synagogue, dating from the mid-1800s, can’t be missed. The Byzantine-Moorish–inspired white-and-red-brick structure, located on a main thoroughfare at the edge of the Jewish Quarter, was heavily damaged during World War II and restored in large part through private donations (Hungarian-born Tony Curtis, Estée Lauder and Yitzhak Rabin all contributed to the restoration and memorial). Unique to this synagogue is the small graveyard beside it (in Judaism, graveyards are usually separate from the place of worship); this is actually a mass grave from the Nazi era, and is kept as a sober reminder. Behind it you’ll find the city’s Holocaust Memorial, a metal sculpture of a weeping willow by Imre Varga.

If you’re not ready to brave Budapest’s bathhouses but are in need of relaxation, head to this small spa on the top floor of the Gresham Palace. There are separate steam rooms for men and women, a shallow lap pool and a divine relaxation area with angled windows that look out over the rooftops of Budapest. A variety of therapies, including body wraps and massages are offered.

This residential and commercial complex is just another of Budapest’s many unique attractions. Seven buildings are connected by courtyards to form a passageway teeming with relaxed cafés and entertaining people-watching. It is especially fun on Sundays, when vendors set up stalls and you can spend hours shopping and eating. Bluebird Café is great for a light breakfast of pastries and coffee, and Spíler (Király utca 13; 36 1 878 1320; spilerbp.hu) is a good spot for an afternoon apertif.

Housed in the massive building that served as the Nazi headquarters during World War II and later of the Communist secret police, this museum is aptly named. It is a powerful and horrific statement about these deadly chapters in Hungarian history, and you should set aside a few hours to visit. The somber entrance hall is dominated by a Russian tank, a reminder of the 1956 uprising, when these immense vehicles rolled down Andrássy Út just outside. The multimedia exhibits feature video and audio installations, along with rooms, including interrogation chambers, that have been faithfully re-created.

Critics have argued that the somewhat flashy displays are too theatrical, and there are moments that feel contrived, like the pitch-dark elevator ride during which a huge flat-screen television plays footage of an old man who describes the almost daily hangings he witnessed under the Nazis. However, simply being in the very place where many of these atrocities occurred is chilling—the cellar with its concrete cells, in particular, is a haunted and miserable place—and the attention to detail is brilliant. Most of the video footage is in Hungarian without subtitles, so be sure to pick up the excellent English audio guide.

Indagare Tip: The House of Terror can be inappropriate for young children, and even preteens and teenagers should go on a case-by-case basis. My visit to the museum stayed with me for days, particularly walking along one long hallway that was covered floor-to-ceiling in black-and-white portraits. As I passed the photos, I assumed I was looking at the faces of those who perished in the 1956 revolution until I spotted two small plaques, one on either side of the hall. The first read “victims,” the other “victimizers”—a terrible reminder of the madness of those times.

Located in the former royal palace, part of Castle Hill, the Hungarian National Gallery is worth visiting for its impressive collection of 20th-century Hungarian art, some of it by artists who, sadly, are underrepresented in Western museums. Skip the first two floors and head directly to the third, where you’ll discover masterful works by Mihály Munkács, Károly Ferenczy and János Vaszary, among others. The top floor houses paintings, drawings and sculpture from 1945 on. The lackluster galleries are badly lit and the walls overcrowded with works, but they do not diminish the genius of a work like József Rippl-Rónai’s haunting Woman in a Black Hat or Károly Ferenczy’s intense Double Portrait.

The best way to view the opulent interior of this magnificent 1884 Neo-Renaissance opera house is to attend a performance (the opera and ballet season runs from September through June). Illustrious directors have included Gustav Mahler, in the late 1800s, and Otto Klemperer, first in 1933 and again after World War II. The quality of the productions varies depending on the director and the cast, but watching a performance from the red velvet–clad, gilded auditorium is well worth the admission. If you can’t catch a performance, there are daily tours, and Indagare members can contact the Bookings Team to arrange a private guide or special access.

While Hungarian cuisine can seem a bit adventurous at times, or at least not as immediately mouth-watering as French and Italian specialties, it offers some of the most flavorful dishes in the world. With the expertise of a local foodie guide, embark on a four-part gastronomic tour; highlights can include the best goulash in town and a visit to local bar for a glass of apricot pálinka, but the tour can be completely customized according to your personal liking (and favorite foods). Indagare members can contact the Bookings Team to set up a tour with one of our preferred guides.

Indagare Tip: Impress your host with your drinking knowledge; Egészségedre is Hungarian for “Cheers.”

Don’t miss walking around the Jewish Quarter, a former Jewish ghetto, whose streets will make you think you’ve stumbled into another era. Despite its appearance, this is Budapest’s most up-and-coming neighborhood, and is a developing center of nightlife, shopping and dining. The city’s famous ruin bars are located here and were quite possibly the catalyst responsible for the area’s current gentrification. The area, located just behind the Great Synagogue, is evocative and teeming with a vibrancy and enthusiasm for life. While in the area, don’t miss Gozdu Court, a residential and commercial complex that is just another of Budapest’s many unique attractions. Seven buildings are connected by courtyards to form a passageway teeming with relaxed cafés and entertaining people-watching.

A tour of the neo-Gothic Parliament, inspired by the one in London and designed by architect Imre Steindl, should be on every first-time visitor’s list. The best way to visit Parliament (security is tight and reservations must be made in advance) is by touring with a private guide (contact the Bookings Team to arrange). The sumptuous interiors contain a wealth of decorative ornamentation; intricate details include the rows of numbered wavy gilded-metal strips that served as cigar holders so that representatives had a place to leave their burning cigars during meetings. The highlight of the soaring Domed Hall, with its 315-foot cupola, is the Szent Korona, also known as the Crown of St. Stephen, which dates from the 12th century and has a wild history (it was kept at Fort Knox after World War II and returned to Hungary in 1978). To fully experience the building’s stunning architecture, visitors should also cross to the Buda side or arrange a river cruise for spectacular views.

Budapest is one of those cities that’s even more stunning when seen from the water. Géllert Hill and majestic Castle Hill, with its striking white Fisherman’s Bastion and Matthias Church, rise on the Buda side. On the Pest side, the waterfront is dominated by Art Nouveau and 19th-century palaces, as well as the neo-Gothic Parliament, whose fanciful façade, reflected in the Danube, is one of the world’s most stunning works of art.

As in Paris, it’s a joy to get up close to the city’s bridges, especially the imposing Chain Bridge and the delicate Elisabeth Bridge (named after the Austrian empress Sisi, who loved Hungary and spent much time in Budapest).

Indagare members can contact the Bookings Team to arrange a private river cruise.

Ruin bars, originally meant to provide locals somewhere cheap to drink, have blossomed into a vibrant form of cultural expression. Housed in derelict buildings in the Jewish Quarter, they are known for their Dr. Seuss décor, with quirky touches like hammocks and spray painted cars providing seating. Each is unique, and to fully understand the ruin bar phenomenon, it is advised to visit several. Indagare members can contact the Bookings Team to arrange a tour of the city’s best ruin bars, from the longtime classics to local favorites, and even to organize a private party in one.

This imposing neoclassical church, named after St. Stephen (István), the first Hungarian Christian king, is just around the corner from the Four Seasons Hotel Gresham Palace. Its soaring, 315-foot dome is one of the city’s most famous landmarks, and through the spring and fall, you can climb the 364 steps or take an elevator to the top for expansive city views. It offers a trove of Hungarian art and religious relics, so it helps to go with a guide (for example, most tourists miss the Chapel of the Holy Right Hand, where St. Stephen’s mummified right forearm is kept). Indagare members can contact the Bookings Team to arrange a visit with one of our preferred guides.

Hungarian designers are on the rise, and Indagare can arrange a visit to the city’s best showrooms, a private fashion show or a fitting in your hotel room before a night on the town. Indagare members can contact the Bookings Team to arrange a fashion-forward tour.

Like its sister cities, Prague and Vienna, Budapest is a place thoroughly steeped in a musical tradition, from the moody melodies of Franz Liszt and revolutionary rhythms of Béla Bartók to the contemporary compositions of György Kurtág. There are numerous concert venues, including the Hungarian State Opera House, the Palace of Arts and a number of churches, like St. Stephen’s Basilica and Matthias Church. But if you only have time for one night of music, catch a performance at the Liszt Ferenc Academy of Music. The three-story neo-Renaissance building and its nondescript lobby are a bit rundown, but the main auditorium is a Secession-style marvel with a gold-adorned ceiling, frescoes and mezzanine seating, as well as an immense organ that presides over the intimate stage.

Founded by Liszt in 1875, the Academy is one of Europe’s most prestigious musical venues—it has produced pianist András Schiff, among others—where most of the performances are by current students. The last time I went, an angelic-looking young woman did a marvelous rendition of Schubert’s Fantasie, a devilishly difficult piano piece for four hands, which she performed with her professor, who could not stop beaming as she took her bows to a chorus of well-deserved bravas. Be sure to reserve tickets well in advance, as the academy is popular with locals.

Think of the two-mile long Margaret Island—named for Princess Margaret who lived in a convent here in the 13th century—as a grander version of New York’s Central Park: a verdant respite from city life, especially during the hot summer months. The car-free island, located north of downtown Pest and reached via the Margaret Bridge, has some sights, including a 187-foot Water Tower, built in 1911; a rose garden and Japanese garden; the remains of a 14th-century Franciscan church; and a huge public swimming pool, designed by Hungarian Olympic athlete Alfred Hajós, who also created the Andrássy. But most people come to jog, walk or picnic on the island’s large lawns and along its leafy shore during the day—it is not advised to go to Margaret Island after nightfall.

The jewel of Castle Hill, a white beauty whose colored-tile rooftop is visible from miles away, has a long and fascinating history. Founded in the 13th century after the Mongol invasion, it was redesigned as a Gothic church in 1387. During more than a century of Turkish occupation, starting in 1541, Matthias Church was converted into a mosque and much of its original décor and ornamentation destroyed. After the Turks were defeated in 1686, restoration began, but most of the splendid interior was restored thanks to the Hungarian coronation, in 1867, of Austria’s emperor Franz Joseph and empress Elisabeth. Franz Liszt composed and conducted his Coronation Mass for the lavish celebration (though he was famously snubbed and not invited to the subsequent festivities because he was not an aristocrat). The church still hosts fabulous free concerts—try to catch a performance by the acclaimed choir.

Memento Park is a must for anyone interested in learning more about the Communist propaganda machine. Instead of destroying the massive statuary after the fall of Communism in 1989, the city placed them in a park in the XXII district (about a fifteen-minute drive from the city center). They include monumental statues of Lenin, Marx and Engels. The sense of history is palpable.

Established in 1872, the Museum of Applied Arts in Budapest is on par with those found in Vienna and London. The fanciful Art Nouveau building alone warrants a visit for its roof, which is decorated with green and golden tiles (made by local Zsolnay manufactory), and the soaring Glass Hall, which looks like the inside of a delicately tiered wedding cake. It was designed by pioneering architect Ödön Lechner, who had a preference for combining typical Secession motifs with elements of Hungarian and Turkish folk art. The museum’s permanent collection features furniture, metalwork, ceramics, textiles and glassware, and there are also great temporary exhibits.

The Old Town, with charming cobblestoned streets and colorful houses, is one of the most polished neighborhoods in Budapest (and while many are private homes, every house has a plaque that describes its origins). After touring the Royal Palace area, with the Hungarian National Gallery and Matthias Church, walk to the Old Town for excellent restaurants like Café Pierrot and Ruszwurm.  In summer, the little cafés spill onto the sidewalks, creating a relaxed ambiance (but beware of the many tourist traps).

Opened in 2005, on the Pest side of the Danube (a ten-minute drive outside the city center), the Palace of Arts houses several cultural venues, including the Ludwig Museum of Contemporary Art, the Festival Theatre (mostly used for chamber music) and the Béla Bartok National Concert Hall, which boasts state-of-the-art acoustics and is the new home of the Hungarian National Philharmonic Orchestra.

Blessed with natural hot springs and thermal spa waters, Hungary has one of Europe’s oldest wellness cultures, and Budapest alone has more than 100natural springs. Széchenyi, located in City Park, is the most famous bathhouse, and a must for any first-time trip to Budapest. That said, to avoid spa culture shock, here are a few things to keep in mind before you go (and don’t worry, bathing suits are compulsory):

• For Hungarians, the bathhouse experience is more about medical well-being than about spa pampering (at one bath house, there is one window solely for Hungarians bearing doctors’ prescriptions). Most Budapest locals I spoke to said they went at least once a week.
• Some bathhouses are unisex
• The bathhouses are vast complexes that hold numerous thermal water plunge pools, large indoor and outdoor swimming pools, massage rooms and changing areas. Some also have pungent sulfur springs baths. Ask a bathhouse staffer to give you an overview before you enter.
• “Hot springs” means just that: some of the plunge pools can go to 100 degrees Fahrenheit
• In most bathhouses, you can buy a half- or full-day pass. Treatments like massages come at an extra cost.

The most well known Hungarian wine is the white dessert wine Tokaji, but with 22 wine regions, Hungary boasts diverse varieties. The region of Etyek is known for fresh, acidic white wines, while Budafok is one of the most historic wine lands in Hungary, and home to the largest underground wine cellar system in Europe. Indagare members can contact our Bookings Team to arrange a trip to these regions, both less than 30 minutes from Budapest.