For all the party people out there, I don't think Vienna is the place to go if you're looking for an all-weekend night out and about. Nevertheless, when I was there for a weekend, I had a most interesting and fun night at a gay night called "Heaven" (Music - Minimal, House etc. - no pop etc.).
Generally, I suppose whoever visits Vienna is going to be stunned by the never ending decadence you encounter there. You'll see a entry with ornaments, fin-de-siecle style buildings, expect a government office behind and it turns out to be just a house entrance.
Of course, you can't miss the Hofburg Palace, Stephansdom or the Opera. I highly recommend to book tickets at the opera with view restrictions for 10Euro. You get what you pay for, but the interiour of this amazing building is simply stunning - and so is the music.
If you venture out to see the famous Hundertwasserhaus, you'll find a sign guiding you to the "toilets of modern art", down there my friend found this amazing (free) map to gay Vienna. Though, I'm sure you can find that brochure anywhere ;-)
For the thrill-seekers or at least friends of fun fairs, you should go to Prater and indulge in numerous rides, cocktails on artificially created beaches or just go for a walk in the enormous park.
Food - Sacher cake at Hotel Sacher with a Viennese Melange is a must, so are the the traditional Austrian Kaiserschmarrn and the Apple-Strudel.
On the whole a perfect place for a weekend break, but even for longer, there's plenty to see and if I had to summarise the city in word it can only be: Decadence.