Must see sights in Vienna?

I strongly recommend that you get Ricks book on Vienna to give you an idea of how much there is to see in Vienna,hopefully your hotel is near the center of town for access to the major sights.
Mike

Vienna has a huge number of sights, many of which will be "must sees" for someone but not everyone. We'll be able to come up with suggestions if you can give more detail of your interests. Are you into palaces, museums, parks, food? Any hobbies? Any particular periods or styles of art that you particularly appreciate?

Agreed that you should read up in Rick's book and see what most interests you. For me personally, I would not miss going to a heuriger (a family run vineyard and restaurant on the outskirts of Vienna, easily reachable via public transportation), Schonnbrunn, the Kunsthistoriches Museum, the Hofburg, the Opera (even just the tour), or St. Stephen's Cathedral. And that's just to name a few.

If the weather had allowed it on the day I visited, I could have stayed until evening wandering around the grounds at Schönbrunn, including the zoo.

This will get you started in your research re must see sights:
http://www.ricksteves.com/europe/austria/vienna

Be sure to visit a cafe for coffee and a pastry. We enjoyed Demel so much that we returned another day to try other sweets.

You've gotten some great suggestions. I also enjoyed the Haus der Musik.

Rick Steves' guide is a superb starting point.

Spend some time in the cafes -- Aida if you want the kitschy, modern feel (and they're everywhere); Demel for some of the high class. Even if you don't drink coffee, the people watching and relaxing are well worth it!

I also highly recommend the Nachtmarkt (night market) for a lot of local flavour.

For some ambience and to 'get in the mood' watch The Third Man, then download the music.