For some art, check out Dabls Mbad, Norwest Gallery, The Heidelberg Project, and any gallery on the Avenue of Fashion — the commercial district on Livernois Avenue south of 8 Mile Road. To learn some history, go to the Detroit Historical Museum (especially the “Detroit 67” exhibit, top floor) and The Wright.
If you’re into tabletop gaming, check if Opal Grove Games has a game night going on.
And for fun events, the news outlet I work for publishes a roundup of things to do every Thursday. I’m biased, but it’s super helpful.