What are your historical interests? I found a few unexpected treasures on my trip there last week:
- Virgilkapelle (chapel/crypt from about 1200 and lost for centuries) located in the Stephansplatz Ubahn station.
- Neidhart Frescoes, on Tuchlauben. Amazing frescoes from a banquet room, painted in about
1399 and rediscovered in 1979. Very rare, secular art.
- The Romermuseum, showing the city's history as a Roman settlement in ~100-500 ACE.
- The open-air museum of uncovered foundations in Michaelerplatz. Working on the Ubahn, they uncovered an area with
overlapping foundation walls from three separate eras. They're on display now.
All of these sites, taken together, will give you an appreciation of Vienna's long history--it was a Celtic settlement before the Romans even got there. It seems like every time they go to renovate a building or dig a foundation, they find evidence of the past. All those pretty, fluffy, Rococo and Baroque and Biedermeier and Jugendstil buildings are on medieval foundations, if not even older ones.
Personally I am meh on palaces and royalty. They make me angry. I'm a lot more interested in the everyday lives of regular people. You'll see the biases of the Hapsburgs in the Kunsthistoriches Museum (which I still wholeheartedly recommend.) Take an extra hour and visit the stone age area of the Naturhistoriches Museum opposite the Kunsthistorichesmuseum for a rare peek into the lives of humans in Europe tens of thousands of years ago. It's rare to see artifacts like these in America; you really have to go to Europe to see them.
The Belvedere has a great exhibit on Klimt and Schiele, which gave me a new appreciation for them. But there's a piece sort of missing: right now, most of Richard Gerstl's work is in New York at the Neue Galerie. If you can, stop in and see that museum on your way to Vienna. The Belvedere also has an exhibit right now on Klimt's classical inspirations, but if you go see that, be sure to go to the Secession either right before or right after, because the Eroica frescoes are a pivotal part of that exhibit (so much so that they've created a partial replica at the Belvedere.)