Minneapolis is a fantastic city. I haven’t lived there for awhile, but I’ll give you some ideas. First - pick up a CityPages, the local alternative weekly. It’ll have all the music, movie and theatre stuff.
Theatre and music are huge there, and you’ll be pretty close to the Orpheum, the Guthrie, Symphony Hall, and a bunch of other theatres that I can’t remember right now. My favorite Minneapolis stat is that there are more theatres per capita there than anywhere else save NYC. I believe it too.
Tons of museums, too. The Walker Art Center is near where you’ll be - they just remodeled it a few years ago. If it’s warmish out you can check out the sculpture gardens. Also the Minneapolis Art Institute is just a few miles south of you, and it’s great too. If you’re into purely modern art, the Weissman Art Museum on the U of M campus is cool.
For fun, hip little areas, there’s Nicollet Mall downtown (one street over from your hotel). Well, I don’t know how hip it is anymore, but it’s a great pedestrian mall where you can shop or catch about a billion busses. There’s also Uptown, which is a several mile long stretch of Lake Street, a couple miles south of downtown. Lots of good bars, weird shops, ethnic food, and indie theatres (movie and otherwise). The U of M campus has a few other little neighborhoods with a similar vibe that are less built up, like the West Bank of campus, and Dinkytown.
Public transportation is pretty decent. The light rail was put in after I left, but I know it’ll take you from downtown to The Mall of America (hideously overrated, imho, but maybe that’s just because I went to high school a couple of miles away). You can get a cab, though I’ve never tried to just hail one. I’d call ahead of time.
The park system is fun, but they just got a bunch of snow, so that’ll probably be out. But don’t forget about St. Paul. I don’t know it as well, but the Science Museum there is truly amazing. They just rebuilt it a few years ago, and it’s hands-down the best museum I’ve ever been to.
Can you tell I’m homesick? I hope this gives you some ideas!