Where in Michigan are you staying? Not all the things I've listed will be accessible if you'll be in Northern Michigan.
It's going to be pretty cold ... but here are some things that I remember that I used to do when I lived there:
1. The Detroit Symphony Orchestra is fabulous.
2. If you like history, try the Henry Ford Museum and/or Greenfield Village.
3. One of the best restaurants in the city (and very fancy) is the Whitney. There are other great restaurants in downtown Birmingham.
4. Shops in downtown Birmingham are fun and there are lots of little restaurants too.
5. There are many small art galleries in downtown Birmingham.
6. The Franklin Cider Mill still might be open when you're there.
7. There's a Museum of Art in Detroit that is quite large.
8. If you'll be in northern MI, Mackinac Island is fun.
9. If you don't mind the drive, go to Frankenmuth -- it's a town where they do Christmas 365 days a year (or maybe 362, something like that).
10. Take a ride in Grosse Pointe and check out all the mansions lining the lake.
That's all I can think of at this second ... maybe I will come up with more, but it's been 11 years since I left MI for CA!