I was there about a year-and-a-half ago, took the Friday night train from Nuremberg, via Munich, and then back again Sunday afternoon.
Of all the places I went to, Vienna was the most like what I expected an old European city to be. The parts I went through were very well preserved, and looked like they hadn’t changed much in decades, or even centuries. Which I think is what DMark hinted at, there isn’t that sense of activity and dynamism that I associate with a thriving city. It’s like they’ve got it the way they want it and are keeping it just so for the tourists; a theme-park version of a real city. Or maybe I just didn’t get around enough.
I rode the Riesenrad, the big ferris wheel seen in The Third Man (and The Living Daylights). Interesting landmark, and a good view of the city.
Took a tour of the Winter Palace. I tend to think of royals as pure figureheads, but there were meeting rooms where the emperor would actually meet with his subjects. And lots of displays about Archduchess Elisabeth, sort of a nineteenth-century Diana.
Near Schönbrunn Palace is the science and technical museum. Very good, if you like that sort of thing. (And I still want to know what was driving that perpetual motion machine on the first floor.) Oh, if you go there, would you pick me up some postcards?
Most of all, walk through the park, take the trams and subways, speak the language as much as you can, and just be part of the city.