Went to business school at UM in 2018. In AA, my go to is Grizzly Peak, a brewpub with great beer/food. Conveniently located on the edge of downtown AA. Homes brewery has the best beer in town, but is a couple miles from downtown. I'd highly recommend if you're looking for good beer. (They also have good Korean BBQ). When I visit, I make sure to hit these two spots.
Wolverine state brewing may be a good spot for the derby (always a good game day atmosphere), but the beer isn't as great as Homes. Conor O'Neils- the Irish pub in town-is probably a good place to catch the Derby as well. I used to watch soccer games here and it was a pretty lively atmosphere (also had live music at night). Hopcat, a local chain, is in the middle of downtown, and has a nice variety of beer/food too. The Raven is a nice whiskey bar, if you're looking for something 'classier'. All of the above have less of a college (ie, Northgate) feel. If you're looking for that, stay closer to campus and see the Brown Jug, Garage Bar, scorekeepers, or good time Charley's. Expect everything to be crowded graduation weekend.
FWIW, I think Zingermans Deli is overrated. Prices are high, and I didn't think the food was as good as everyone else thought. It has its charm because it is an AA original. As an alternative, try out Zingermans Next Door Cafe. Get a nice coffee/pastry, but save the headache of the original place.
In Detroit, cork town has some nice watering holes. Nemo's was where I'd go to catch an Aggie game (the owners son, maybe nephew, was in the Corps at A&M, so you'll see an Aggie helmet sitting next to all the Big 10 helmets lol), and the beer and food are solid. Same for Mcshanes Irish Pub- I went here a few times before Tigers games- solid food/drink.
I second the Henry ford museum. Up there with the Smithsonian's IMO. Also, walking along the Detroit river is something I did when I'd visit the city. Weather is, usually, pleasant this time of year and there are enough bars/restaurants close by when you need to stop in.