I live a little north of Detroit. Great place to live, lots of fun stuff to do. Some really cool architecture. Things have changed since I moved here in 2009. Some run down parts of town, but no worse than any of the other big cities I’ve lived in.
Ann Arbor is a nice college town. I work there periodically, and it’s a fun place to visit. The big house is a great place to watch a game. I take my son to a game every year, and it’s always a good atmosphere.
Detroit isn’t particularly close to AA, and the game day traffic can be bad. If you don’t plan to get there really early, 14 can be a tough slog. If you can make it work in AA, I would.
If you’re just looking for a cheap place to stay, Ypsilanti is a drab town, but it has a state university, Eastern Michigan. I bet there will be hotels there, and it’s much closer than Detroit. Lansing is about equidistant to AA relative to Detroit. It’s not a town I enjoy visiting, though MSU has a beautiful campus. Another option.