You should have gone to Michigan Ohio state and skipped aggy haha.
Ann Arbor isn't a small town, it's a full blown city so you can get on Google or yelp or whatever and find stuff. For gameday specifically you should find a tailgate to pay for and just do that. Generally mgoblog has one and there's one from an alumni association or something.
You want to stay on the south and west side of the stadium mainly on game day. South you can check out the golf course tailgates and west is all the student parties and lots of other tailgates.
Stadium and main is where all the action is and its a cool approach into the stadium.
North on main you get to downtown after a good walk, it's not really worth doing on gameday, I would go do that the night before. Zingermans is the regional place that you should eat one meal at. Bread is their thing, so get a bread dish of some kind their sourdough is incredible.
Ann Arbor is a lot of fun and so is Detroit. I would go in Thursday or stay over Sunday there and check out greektown, belle isle, the people mover, Detroit tigers stadium, the Caesars arena. All cool and there's eminems spaghetti restaurant called moms spaghetti.