Hi, Jodi -
Based on three short visits in Vienna, here are some things I would suggest:
1. Walking. From your location, it should be possible to walk all the way to downtown --the area around the Cathedral, Graben, etc. Vienna has lovely parks everywhere - great for strolling or for sitting when you're tired.
2. St. Stephens Cathedral - definitely worth a visit.
3. Get a good map and look for the walking/bicycling path that runs along the Donau Canal. This is also a wonderful way to be in the city without being overwhelmed by it.
4. Museums, of course...but if you're just there for three days, and the weather is good, I recommend being outside to get a feel for the city.
The trams &the subway work off the same tickets - buy a strip of four (or more) from a machine in the subway stations (or from newspaper/tobacco/miscellaneous kiosks near tram stops) and go where your interests lead. My pension (the Baronesse, near the University) was on a tram line that ran from the West Station to the Prater amusement park/garden...very handy. Prater is worth checking out, if only for the giant ferris wheel.
Rick Steves has some good suggestions for the city. It's a lovely place - enjoy it!
Julie in Seattle - (count me in for a northwest GTG, if it's still in the works.)