The gothic St. Stephen's Cathedral (Stephansdom) defines the skyline of Vienna, with its huge bulk and colorful tiled roof, bearing the Habsburg coat of arms. Visit the catacombs, or climb 343 steps to the top of the south tower to enjoy 360 degree views of the city to the Vienna Woods beyond. (Stephansplatz 1; open 8:30 a.m. to 8 p.m.)

The Museumsquartier (Museumsplatz 1), a redevelopment of the 18th-century imperial stables, is a collection of superb museums. The cultural district features the Leopold museum (open 10 a.m. to 6 p.m., Thursday 10 a.m. to 9 p.m., closed on Tuesday), the Museum of Modern Art (open Monday 2 p.m. to 7 p.m., Tuesday to Sunday 10 a.m. to 7 p.m., Thursday to 9 p.m.) and the Kunsthalle (open daily 10 a.m. to 7 p.m.), an exhibition center. The whole complex contains bars, restaurants and grassy areas, and during the summer, hosts live events, from bands to fashion shows.

The Haus der Musik is one of the finest interactive museums in Europe, exploring the history of Vienna in the context of classical music. There are scientific rooms to demonstrate the physics of sound; rooms where you can compose your own melody and have it played by an orchestra; rooms dedicated to the most famous composers (including a poignant exhibit where you can experience Beethoven's decline into deafness); and the highlight, a chance to "conduct" the Vienna Philharmonic. Warning: If you're not up to snuff as a conductor, you could be booed off by the virtual orchestra.

The Spanish Riding School, one of the world's most famous schools of equestrian art, is closed in July when the renowned Lipizzaner stallions go out to grass, but you can get tickets online for training sessions and performances at other times of year. (Michaelerplatz 1; open Tuesday to Sunday 9 a.m. to 4 p.m., Fridays when there is a performance 9 a.m. to 7 p.m.)

Hear the Vienna Boys' Choir sing every Sunday at the Hofburgkapelle (Hofmusikkapelle, Hofburg) apart from in July and August, when they're on summer break. Tickets are in great demand; book early.

In April, May, June and September, anybody can watch one of the approximately 150 performances at the Vienna State Opera for free on a giant screen outside the opera house on Herberg-von-Karajan-Platz. Attendants even provide rugs for spectators to sit on.

At Schonbrunn Palace, you can tour dozens of rooms, including the magnificent apartments once occupied by Emperor Franz Joseph and his wife Elisabeth, as well as those that belonged to Maria Theresa, the powerful Habsburg ruler. Outside the palace are sweeping Baroque gardens, fountains, a maze, greenhouses, a carriage museum and even a zoo.

Take a trip out of town to the Zentralfriedhof, one of Europe's biggest cemeteries, with more "residents" than Vienna itself. This is not as macabre as it seems. The cemetery is exceptionally tranquil and beautiful, with impressive Art Nouveau architecture, and all the graves of the city's famous musicians are clustered together: Beethoven, Schubert, a memorial to Mozart (who was buried in a pauper's grave) and the entire Strauss family. (Opening hours vary by season; summer hours are 7 a.m. to 8 p.m. daily.)

Check out the Naschmarkt, the city's most colorful food market, with all kinds of artisan products. Try a balsamic tasting or munch on Vietnamese spring rolls. In summer, buy giant peaches and bunches of plump cherries for snacks. (located just outside the Ring; open early daily.) There are some great, quirky shops nearby; designer vintage at Flo Vintage on Schleifmuhlgasse, or handmade herbal remedies at Saint Charles Pharmacy on Gumpendorferstrasse.

Visit the Prater, the world's oldest amusement park. The park is a huge green space used by the Viennese for recreation outdoor activities, such as picnics and cycling, as well as for the many rides. It's open 24 hours a day, seven days a week, year-round. Individual attractions have their own opening hours, and you pay for each ride individually with fees starting around 1.50 euros. The biggest attraction is the giant Ferris wheel, the Riesenrad for spectacular views across the city. It's open in summer from 9 a.m. to 11.45 p.m. The Prater is easily accessible by subway (U-Bahn), with Praterstern on the U1 line the closest stop.

Stroll the streets of Spittelberg, the up-and-coming district just beyond the Museumsquartier. The neighborhood features beautiful Biedermeier houses and hidden squares. This is one of the city's main art and design districts, with trendy cafes and small, one-off boutiques.

Take a Third Man tour, following the locations of the famous 1949 Orson Welles' film, including the city sewers and the famous Riesenrad (Ferris wheel) in the Prater.