hi there!
i live in vienna and probably know a few things ...
you should definitely visit either schönbrunn or the belvedere. though schönbrunn is the famous and big place to go, belvedere is some kind of little brother. it's a bit calmer there because not so many tourists know of this place...
stephansdom is also quite obvious. try to climb it if you can
when you're at stephansdon, just take a walk in this area ... it's the central district with a unique viennese flair when you stroll through the small alleys and see those little shops etc ...
prater is actually okay, but i would not go there. it's just an amusement park .
you could definetly go karlsplatz and follow the signs till you are in front of the opera house (Staatsoper). There's a big one-way street called "Ring" that's been the citie's border som 200 years ago. if you walk along it, you will pass quite everything there is to see: parliament, Rathaus, university, national nature and art museum, Hofburg, Burggarten, ...
One of the best things one can do in Vienna is, to drink coffee in an old viennese style coffee house. It will be quite easy to spot one near "Graben" which is an exit of subway U1 Stephansplatz station, but you should definitely go for one of the better ones like Café Griensteidl (Sigmund Freud, Arthur Schnitzler etc used to go there back in the days), Café Central or Café Dommayer (which is situated near Schönbrunn).
Eating and drinking is awesome here. Just check a supermarket for milk products ... you will see that eating in Vienna is much about quality of the ingredients. There are definetly some places to go:
If you want to eat in a classical ambience, you should not miss out on eating viennese Schnitzel (Wiener Schnitzel) at Figlmüller's. Figlmüller serves the biggest (and probably best) Schnitzels in town - you can find it near Stephansplatz at Wollzeile 5.
But if you want to eat a bit more rustical, there are a lot of nice places a bit outside of Vienna. Especially Grinzing district is home to many "Heuriger"s. This is a type of restaurant where you usually sit outside in a garden on some kind of benches around a long table. The waiter only serves self-made wine, beer or non-alcoholic stuff. If you want to eat something you have to go inside the house and choose from dishes they present to you (usually you should try a little of everything here if you are not used to eating "Schweinsbraten", "Blunzen" or "Speckmeisen").
If you want to eat Sachertorte, do NOT go to Hotel/Restaurant Sacher! Though they claim they make the original Sacher cake, their Sacher cake is not that special. Your mouth feels kind of dry when eating a Sacher-Sachertorte. You should go over to Demel's K&K Hofbäckerei who delivered all kinds of pastries and cakes to the king back in the days ... their Sacher cake is also claimed by many historians to be the real original Sacher cake. Their Sacher cake is _MUCH_ better as it has not one, but two layers of marmalade inside - so it's not that dry. (You can find Demel at Graben in the central district!)
Vienna is actually a quite nice city to go shopping. For expensive clothes and international brands such as LV, Diesel, Burberry, you should check out Graben. If you want to check all kinds of other things, there is Mariahilfer Str. (subway U2 - station Museumsquartier;; U3 - station Zieglergasse and Neubaugasse;; bus 13A and 14A station Neubaugasse). There is an Apple shop called "McPro" near the U2 station. If you're taking along a girlfriend, she might be interested in looking at clothes at Neubaugasse.
At night, you should check out "Hermann's Strandbar" near the Urania on Schwedenplatz if it's warm outside ... otherwise just check the first district, there are plenty of bars and pubs.
If you've got any questions, feel free to ask
sorry for my sloppy English, I definitely write better, it's just that I woke up a few minutes ago
