Andratx, on the western edge of the island, is home to the Camp de Mar beach, a favorite of bikini-wearing regulars like Claudia Schiffer. Port Andratx, once a small fishing village, is now an upscale seaside resort. Have a drink and watch the people and boats go by from a waterfront café.

Not all of Mallorca's coastline is beach, but those pockets of sand are stunning and well worth a drive. Some favorites include Cala Mondrago on the east coast and Des Trenc on the southern coast.

Nothing compares to seeing the island by boat, and Indagare members can contact our Bookings Team for help arranging a charter. A highlight is a trip to Cabrera, an island that held a prison during the Napoleonic Wars and is an animal refuge.

This cultural center occupies one of Palma’s most beautiful modernist buildings. It is home to the permanent collection of art and objects of the painter Anglada Camarassa as well as temporary exhibitions.

Take the roller-coaster drive out to the Cap de Formentor, the northernmost tip of the island and home to some of its most dramatic scenery. There are several viewpoints along the way—such as the cliff-top Mirador de Mal Pas—but for the best views, continue on to the lighthouse, from where you can gaze out across the ocean at the neighboring island of Menorca over a café con leche.

A castle sitting on the top of a hill, Castell de Alaro is only reachable on foot (and takes two hours to reach).

Indagare members can contact our Bookings Team to arrange private cooking lessons with a Mallorquin chef. Highlights will include wine tasting, visits to olive oil presses and market shopping.

This museum of modern and contemporary art overlooks the port and displays myriad works by Spanish artists such as Miro, Barceló and Picasso. The museum’s terrace restaurant (serving up fantastic views and gourmet Mallorquin cuisine) and architecture (modern glass and concrete facades that contrast dramatically with the surrounding Renaissance fortress walls) that make the biggest impression.

Some call Fornalutz the prettiest village on Mallorca. Decide for yourself among mountainous views, with the sweet smell of orange blossoms drifting in the air. The town’s sweet cobbled streets and quaint stone houses is an idyllic rural spot, and there are excellent hikes in the surrounding areas.

Housed in the studios where Joan Miro worked for 25 years, this museum is a center for creativity on Mallorca, celebrating the artist and all Mallorquin artisans.

Writer Robert Graves moved to the quiet village of Deià on Mallorca’s northern coast in the 1930s. He lived among the locals while continuing to turn out serious literary works. He died in 1985, and his home has been turned into a museum.

Located in central Palma, Hammam Al Ándalus is, as the name suggests, an Andalusian—and therefore Arab—inspired bathhouse. Guests can choose from a series of signature rituals and wellness treatments, from hot stone bed massages to water and aroma therapies and more.

Recommended by Indagare Insider Oro del Negro.

There is excellent hiking throughout Mallorca. One favorite is the Sa Calobra leading down to Es Torrente de Pareis.

Nestled in the Tramuntana Mountains, about an hour's ride from Palma en route to Soller, lie the Alfabia Gardens. The UNESCO World Heritage Site comprises a house, garden and orchard, and provides a tranquil oasis from the heat and crowds. Within the gardens are a variety of trees, including indigenous Mallorcan palms and an array of vibrant flowering plants. With its scenic views, jasmine-scented paths, and lovely fountains, Alfabia Gardens is a lovely place to explore. The estate was once home to the Arabic Viceroy of the island, and the Moorish-inspired architecture, garden design, and irrigation canals throughout, certainly evoke such a presence. There’s also a small cafe for a bite and a break. The gardens are open every day, even Sundays when many other places on the island are closed.

It’s impossible to miss Palma’s vast 700-year-old cathedral, which lords over the horizon. The interiors were restored under Antoni Gaudí’s direction in the early 1900s and continues to be updated even today. In more recent times, the famous Mallorquin artist Miquel Barceló created an enormous ceramic mural of the story of creation, which covers the walls of one of the cathedral’s lateral apses. There is a museum but if you want to see the cathedral's interior, attend a Sunday mass.

The former home of artists Yannick Vu and Ben Jakober has been transformed into a foundation, to share their art-filled home and collections with the public. Located on an enormous property on a peninsula on the eastern end of the island, Sa Bassa Blanca Museum can best be described as a cultural wonderland that encompasses a house, garden, art collections and a sculpture park. The Moorish-style mansion is a gem in and of itself. Designed by Egyptian architect Hassan Fathy, and with ornate details throughout—hand-painted tiles, a Mudejar coffered ceiling, Moroccan panels—it is filled with eclectic art from a lifetime of collecting. Museum spaces include the Nins Collection, the old master's collection of more than 150 portraits of children that they began after their own daughter died at 18; a second underground space showcases contemporary works; the “Zoological Park” sculpture garden with giant granite animals by Vu and Jakober; and the Sokrates Space, conceived as a giant cabinet of curiosities with contemporary art pieces including a James Turrell installation.

There is so much to take in that Sa Bassa Blanca is best navigated and appreciated with a guide. The museum can also be somewhat difficult to get to. Located in a protected natural area, down an unpaved road, there is no public transportation to reach the museum, and it can be tough to get an Uber for your return. Nonetheless, it is worth the effort—just plan transportation ahead.

Down on the sea front, contemporary art lovers have another space to explore—the Palau March museum showcasing works by world-renowned sculptors like Henry Moore and Rodin.

Explore the north coast and wander Pollença’s charming narrow streets. You will find quiet squares and open-air cafes, and you can climb the 365 steps to the Calvary chapel, the site of a dramatic parade every year on Good Friday. Every year in July and August, Pollença hosts a lively festival featuring several classical concerts. Past festivals have included performances by the London Symphony Orchestra and Boris Berezovsky on the piano. It’s one of the most popular music festivals in Mallorca, so advanced booking is highly recommended (www.festivalpollenca.org).

South Beach meets Ibiza at Puro Beach. It’s easy to spend the whole day at this glowing white beach club–restaurant–spa, which juts out into the bay like a small peninsula. Make sure to arrive early and reserve a lounge chair, then have a leisurely poolside breakfast or a light lunch. Before cocktail hour, sign up for an open-air massage at the spa. Despite its location outside the city center near the airport, PuroBeach can be booked days in advance for dinner. Dishes include an international mix of grilled lobster, lamb kefta and moules frites. Puro Hotel offers a Puro Shuttle to PuroBeach. Guests of the hotel have priority.

This monastery was home to the composer Chopin when he composed the majority of his preludes.

Wine lovers shouldn’t miss Mallorca’s many exciting young vineyards, such as Bodegas Anima Negra (pick up as many bottles of its top red wine, AN, as customs will allow) and Finca Son Bordils. Indagare members can contact our Bookings Team to arrange a full- or half-day wine tour, makes visiting these estates fun and easy, especially if you can’t speak any Spanish.