I'm just curious; how did you become a Michigan fan? Is it in your family?
My favorite establishments in AA are Ashley's on State St, Grizzly Peak Brewing on, uh, Ashley, and Arbor Brewing on Liberty (yes, I'm a beer person). I would check out those places but there are dozens upon dozens of GREAT pubs and restaurants in downtown Ann Arbor to go after the game. Before the game I would hang out around the UofM golf course right across from the stadium. That's really where the best atmosphere is in my experience. If you don't mind paying $25+ there's plenty of parking either there or across Main St at Pioneer High School.
Also, kind of a unique thing about The Big House is that you never really see it until you're right there. It just kind of pops up on you. Although now with all the rennovations it really is quite a sight as you approach.
Post again after you come and let us know how your first day in Ann Arbor/at the Big House goes.