Virtually all guidebooks identify the city's major sights: Stephansdom, the Hofberg, Belvedere Palace, Schönbrunn Palace, Kunsthistorisches Museum, etc. Each, of course, is a "must see" and worthy of your time. At the Hofberg, be sure to visit the Schatzkammer and at the Belvedere—you've-seen-the-poster-now-don't-miss-the-real-thing—Klimt's famous Der Kuss (The Kiss).
Over the years we've often mentioned our personal favorites but perhaps a few bear repeating. Though a tad creepy, the Capuchins' Crypt or Kaisergruft, which holds 100-plus fabulously ornate coffins of emperors, empresses and archdukes (but only the bodies are here; the hearts are in the Church of Augustinians and the entrails in the catacombs under St. Stephen's) is a palpable connection to the days of empire.
Conceived by artists who "seceded" from what they considered false values of the times, the Secession building is a famous symbol of the Jugendstil/Art Nouveau movement. Derided when built in 1898, its dome was compared to a cabbage. In the basement see Klimt's visual interpretation of Beethoven's 9th Symphony.
The most tangible element of Vienna's greatness is its buildings. One of the most intriguing is the Hundertwasserhaus, an uneven, quirky apartment complex that looks like it could have been concocted by a clever fourth grader. Friedensreich Hundertwasser also designed Vienna's KunstHaus, which exhibits his work and that of such 20th century artists as Joan Miro, Marc Chagall and Picasso. Hundertwasser, who died in 2000 aboard the Queen Elizabeth II, was a rule-breaker; square corners can be round and places that convention says should be level often are not.
The Flohmarkt, a wild collection of people and central European antiques and curious remnants, makes an ideal Saturday morning stroll.
Several of the world's greatest musicians and composers came to the end of the road in Vienna. Take the tram to the Zentralfriedhof (main cemetery, Simmeringer Hauptstrasse, section 32A) and visit the graves of Beethoven, Schubert, Brahms, Johann Strauss, and others. Don't look for Mozart, he's buried in an unmarked common grave, the whereabouts of his remains are unknown. There is an empty tomb in his honor at St. Mark's cemetery (3rd dist., Leberstrasse 6-8).
And, finally, we once spent a pleasant hour in the Uhrenmuseum (clock museum)