I just moved from Ann Arbor (lived there 99-04). I miss it so. The town is pretty much tied to U of Michigan, which always has something going on, so check the student newspaper. (
www.michigandaily.com)
Museums:
UMich has multiple museums open to the public, all within walking distance of each other:
Museum of Anthropology
Museum of Natural History
Museum of Paleontology
Museum of Zoology
Kelsey Museum of Archeology
Museum of Art
Sindecuse Museum of Dentistry (hehe)
Nichols Arboretum (very fun place to visit in the fall)
Entertainment/Nightlife:
Back in the day The Necto was a great nightclub, with a solid retro night and solid techno/house night, though I'm not sure how good it is anymore.
Goodnight Gracie's & Bab's are fantastic martini bars. Gracie's often has live jazz or techno. Bab's is extremely comfy, intimate, dim, smoky - the way a martini bar should be.
The Firefly Club is a jazz bar that brings in lots of great musicians, and has good, stiff drinks.
The Heidelberg is a good German restaurant. The Club Above (the club that's above the Heidelberg, hehe) also has some good stuff going on from time to time.
The Blind Pig & Ark usually have at least one or two good live shows a month, from hip hop to alt rock to blues.
Conor O'Neill's is an Irish pub that has good food and is a great bar.
Ashley's is also a real chill place.
Restaurants:
Zanzibar is a fantastic African restaurant.
Raja Rani is a really good Indian restaurant with a cheap buffet style lunch.
Palio is a very solid, very consistent Italian restaurant.
Zydeco is a great Cajun/Creole restaurant.
South University has multiple hole in the wall eateries, including a great Middle Eastern place that has fantastic kebobs & gyros; I ate there probably three times a week for two years and can't remember its name, haha.
Dominick's: quite possibly the best place to hang out with your friends. It's an open air restaurant with good food and killer sangria (I had to walk home from there more than once, hehe).
Sports:
Take your pick - Michigan is in the Big Ten, so there's no shortage of collegiate level sports going on.
If all else fails - remember you're about 25 minutes down the freeway from the heart of Detroit.
Have fun, hopefully I'll be back in another year!