Not sure how much time you'll have besides what seems like Saturday afternoon. If you have Friday open, here is the list that I've done the last two times I've gone back home. Lunch at Supinos, then a couple beers at Slows, then to happy hour at Roast, a drink at Cliff Bell's, wander over to D'Mongos for a drink, then finish it up with either a chicken schwarma sandwich at Bucharest Grill/Park Bar or a coney at Lafayette.
Now, if you don't have a full Friday to devote to imbibing, Supinos is really, really great pizza. Oh, and get the cannoli. Even if you don't normally like cannoli, get the cannoli (I would just get it with some pistachios). Slows. Yes, depending on when and how many are with you, you could have quite a wait for Slows. If you just want some BBQ, they recently opened Slows2Go their take away location. But, I love Slows. If it's just you, grab a spot at the bar and go to town.
If you're looking for Sunday brunch, that's a bit difficult. Not many options. But, when we went to Mudgie's Deli (which I highly recommend as well) they seemed to do a brunch. Also, there is a great little crepe joint in the middle of nowhere (not far from Slows) called Le Petit Zinc. Would be an option, too.
There's a wine bar that I haven't been to, but could be something for people to go to called Motor City Wine (right above a bar called Foran's, which is yet another place to go).
When you're at Eastern Market, find the guy with the beard selling Great Lakes Coffee, his name is James and he's a great resource as well as a great guy. He could even tell you if there are other people down there to meet (like Evan who posts here sometimes).
This should be enough to start. Have a great time.
