SEE ALSO: Day trips: Schönbrunn.

The performances at the Burgtheater—known to serious theatergoers simply as “Die Burg,” and considered one of the most acclaimed stages in Europe—are in German. But Klimt fans should take the forty-five-minute backstage tour to see the two ceiling murals the twenty-six-year-old artist created with his brother, Ernst, and fellow painter Franz Matsch from 1886-1888. Klimt’s opinion of the finished work was rather harsh (he famously called it Schweinsdreck, which translates to pig dirt), surely in part because Emperor Franz Joseph insisted upon a self-portrait of the artist. If you’re standing under the panel that depicts Shakespeare’s Globe Theatre—the murals portray well-known playhouses and scenes from plays—look for an audience member wearing a white ruffled collar. It was the first, and last, time Klimt depicted himself in one of his works. Tours in English are available Friday, Saturday and Sunday at 3 P.M., and cost $8.

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Austria’s oldest and largest auction house, the Dorotheum was founded by Emperor Joseph I in 1707; today, there are several branches. Its headquarters in a large palais in the Dorotheergasse is a wonderful place to visit if you’re interested in antiques. Weekly auctions focus on a variety of goods, from Biedermeier furniture and fur coats to Baroque paintings and antique jewelry, which are exhibited in advance. Items that are not sold at auction automatically go into the Dorotheum’s permanent sales exhibits, and these floors are of particular interest for bargain hunters, as items are sold at a fraction of their estimated value.

Since being privatized in 2001, the Dorotheum has been openly addressing its ugly role during the Third Reich (Austria was annexed by Nazi Germany in 1938), when possessions belonging to thousands of deported Jews were auctioned off. The new management has realized that a key component of moving into the future is recognizing this terrible chapter (in 2006, a payment of $32 million, as a “General Restitution Fund for the Victims of National Socialism,” was issued), and today, a department researches the provenance of every object sold here.

TIP: If you’re interested in jewelry, skip the displays of new, well-known brands sold on the upper floors and head to the bargain basement. Here, pieces that have been on display for a long time are discounted even more, and you can discover real treasures; on a recent visit I found an Art Nouveau enamel brooch and a beautifully crafted amber ring. Touring the Dorotheum is free of charge. Closed Sunday.

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This huge, sprawling complex—home to the Hapsburg royal family until 1918—includes an embarrassment of riches, like the Treasury and Museum of Ethnology, the Spanish Riding School, Imperial Court Chapel and National Library. There are also the Imperial Apartments and Sissi Museum. Depending on whom you ask, the Hofburg also encompasses the Kunsthistorische and Naturhistorische museums, though they are located across the Ring boulevard (near the MuseumsQuartier).

Guide Diane Naar-Elphee, who has been based in Vienna for some thirty years, says an insider tip is visiting the Hofburg on Sunday morning: “You start the day at the Imperial Court Chapel, where the Vienna Boys’ Choir perform every Sunday at 9:15 a.m. Mass lets out right before the performance of the Spanish Riding School at 11 a.m., so you can watch the horses and costumed riders crossing the road between the stables and the riding school. Then, if you’re in the mood for more classical music, there are free concerts at 11 a.m., mostly of classical liturgical works of Mozart, Schubert, Haydn et al, in the Augustinerkirche, one of the most beautiful churches in Vienna.”

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Occupying the former Imperial Stables, the MuseumsQuartier was much applauded when it opened in 2001, as it added a healthy dose of contemporary chic to Vienna’s somewhat traditional museum scene. Today it houses a vibrant collection of museums, including the Leopold, Museum of Modern Art and Zoom Children’s Museum. It’s a huge complex with good restaurants and cafés, including Milo and Café Halle. There are also several gift shops, particularly MQ Point and Kunsthalle, that carry the work of local designers.

This State Hall was commissioned by Emperor Charles VI to house[rep] the court library, but it’s the 15,000-volume collection of Prince Eugene of Savoy, whose summer palais now contains the Belvedere, that makes it one of the world’s most extensive historical libraries. The space is pure Baroque splendor, with colorful ceiling frescoes, marble statues and nutwood bookcases lining the walls of this 18th-century gem. Don’t miss it when visiting the Hofburg. Closed Monday.

This museum is located in the oldest part of the Hofburg, which dates to the 13th century. One of the world’s most important imperial treasuries, the Schatzkammer holds such invaluable pieces as the gemstone-studded emperor’s crown, from the latter part of the tenth century, and the enameled Austrian emperor’s crown—embellished with diamonds, rubies, sapphires and pearls—from 1602. There are also artfully sculpted gold and silver tableware sets, used by the royal family at state functions (they even took them on trips when hosting dinners abroad). Note how the oversized centerpieces were strategically arranged so that dinner guests could not see across the table and were forced to speak to those sitting beside them.