I went to U of M from 2008 - 2012 so I'm familiar with the area. I'm short on time now and can post more later.
U of M has stricter firearm laws than the state laws. Firearms are banned on U of M property per
ordinances set by the regents. This was
challenged in court, but ultimately a judge
threw it out. Outside of the university, MI has preemption meaning no local jurisdiction can make stricter firearms laws. This means Detroit follows the state laws.
As for hotels, there are some nice ones in downtown, but cheaper rates can be found down by Briarwood mall if you don't mind a 5-10 minute drive to downtown. Briarwood mall also puts you in walking distance (a 2 mi walk or so, but walkable) of the stadium where the game will be played. As was mentioned in the next post, don't even try driving to the game if you stay in a hotel near Briarwood.
Restaurants:
Blimpy Burger (Featured on Diners, Drive-Ins, and Dives; good burgers)
Zingerman's Deli (great deli sandwiches with quality ingredients)
Maize and Blue Deli (good deli sandwiches in the heart of student territory)
Blue Tractor (solid BBQ joint)
Jolly Pumpkin (brewery and unique foods)
Tio's Mexican (good Mexican, and way too many tequila choices)
Hopcat (Crack Fries, enough said; huge beer tap list)
Grizzly Peak (brewery and pub food)
Downtown Ann Arbor has a lot of restaurants along Main St between Huron and William.