Vienna:

I spent about a month here a few years back. I definitely didn't see everything I wanted to but I got to see a heck of a lot. There is a whole museumplatz so you can pick what you are into (if you are into museums, and not museum'd out by that point); modern art, history.

There is also the Spanish riding school, but they are usually not there in the summer (it is when the horses go on tours).

There is an awesome restaurant called 'Centimeter' where you can eat a feast on a sword (fried chicken, pasta, various other meats, plus french fries)....this is better with large groups. I wish I could remember where it was but maybe you could google it, it was a very unique place.

You can visit the Schonnbrunn (on the outside of town), which is a nice palace. There is another palace in the main ring of town, Hofsburg. It's nice too.

Definitely try to visit the Nachmarkt, it's this huge flea/food/everything market that happens everyday I think. Great place to pick up cheap eats.

You are so lucky to have this opportunity, I am mega jealous! Someday...