For starters, my tips are very subjective, but that's obvious, isn't it? So, let's begin.
1. find a place to stay in the centre, or at least at walking distance. Let's just say that I'm not an avid fan of the metro when it comes to tourism. You lose your sense of direction and all those amazing things you could see on foot. Plus, it usually costs you a lot of money. And in Vienna it's kind of superfluous to use it, since it's quite a small town and the usual sightseeing is done in a very short distance. Plus, you have the bonus of being able to walk home at night and not having to use the nightbus. And I know there are some very reasonably priced hostels close to the city centre.
2. Visit the museumsquartier. I've been in love with this pace since my first visit and it hasn't diminished ever since. Even if you're not very fond of museums (which is not my case), it has events, and restaurants and ateliers, and shops and amazing gluhwein in the winter months. A must see.
3. Learn a little german. I was always embarrasingly fond of my languages and thought I could conquer the world with them. But when I went to a lecture of n Austrian architect-writer I couldn't understand a thing. And then, when the conversation with people I've met here went to difficult topics, I comfortably switched to english. But there was a problem with that: not everyone was fluent in english! so, if you'll just do tourist talk around here your english will probably be fine. But if you have other aspirations, it wouldn't hurt knowing a word of german or two.
4. You need cheap, plenty and delicious food? go to dewan! It is a place near the university and very close to the freud museum, in which you can fill (and refill, if you want) your plate with different kinds of pakistani food. After 3 days of expensive eating, this was heaven.
4. Visit the musa. After three days of extensive museum-visiting (when I wasn't busy with the symposium), I can assure you that this was the best art exhibition I saw in Vienna. And the entrance is free.
5. Be wary of the christmas markets (if it's that time of the season). Having been to this kinds of things a lot since I was a kid, I am quite sure that the Viennese ones are on the expensive side (I mean, gluhwein for 4.50? no way!). And since I know that all those chocolate strawberry sticks must look amazing when you first see them, I wouldn't say "don't buy a thing". Just try to be frugal.
6. Walk! As I sais in point 1, Vienna is a small town. And a very beautiful one at that. So walking or biking is the best way to see it. I believe ther are even some free bikes in some corners of the city (but you'd have to check that with someone who's actually tried to use one). There are many roads to take. My favorite one would be from the Museumsquartier to Votivkirche via Herrengasse and Stephansplatz. Another one could be a tour of the Universities, from die Angewandte to the University of Vienna, via the polytechnical school. Or anything else.
7. Drink Booze. I'm not saying you must do that. But sofar Vienna has passed my alcohol test with distinction. It has great local wine, even when it's cheap, great beer and great cocktails. Visit the Loos bar and you won't be disappointed. If you're interested in Architecture, even better. I'm not even talking about the gluhwein, because it's an obsession of mine.
8. Go home early. Clarification: when I say early, I mean by Greek standards. Because I always believe in "doing it like the locals" and being sober while everyone else is already dead drunk is never pleasant.
So, that's it from me. And 9. Don't forget to have a nice time!