I don't know much about Vienna though from what I understand there is plenty to do if you're into culture, history and sightseeing. It isn't a typical tourist destination like places in Spain or Greece, though Austria is a fantastic country and well worth a visit if you get a chance.

Do you know where abouts in Vienna you're looking at staying or does that depend on the suggestions you get here?

Schonbrunn Palace (Schloss Schonbrunn)
Imperial Palace (Hofburg)
Sigmund Freud Haus Museum: Freud's former home contains numerous documents and photographs from throughout the famous psychologist's life.
St. Charles's Church (Karlskirche)
Built around 1715 by Fischer von Erlach, this is one of Vienna's best known landmarks.

Your trip sounds great and it is the perfect time to do it! I wish I could go back to Vienna. If I could recommend something, I would say it is important to travel to other parts of Austria. Don't get me wrong, there is a lot of things to do in Vienna, but it is important to view the rest of the country as well. I stayed at a great hotel about an hour outside of Vienna. I highly reccommend it for a great place to relax.

http://www.travelintelligence.net/wsd/hotels/htls_8027_Wine_And_Spa_Resort_Loisium_Hotel_Langenlois_review.html

I think Vienna is considered more of a relax vacation than anything else. Sight seeing the amazing architecture would be great, I have always wanted to visit this place since I first learned about it! Here are afew things I would try when there, you might think the same: Karlskirche and Kunsthistoriches Museum (both recently renovated), Beethoven Memorial House & the Sigmund Freud Museum..........then again maybe I'm just a geek. :)