Ok, while this is not a comprehensive list, it will get you started. It kind of depends on where you want to go, how far you wish to travel, how much golf you wish to cram into a getaway and of course how much you want to pay. I have left out courses that are on the east side of the state just due to travel time.
There are a few very good areas for golf on the western, central and northern parts of the state. Each has its distinctive terrain. Kalamazoo/Battle Creek is flat to rolling terrain. Grand Rapids and the western side of the state feature pines and woods, to hilly dunes further west. And northern Michigan and Gaylord is simply Michigan golf at its best, with dramatic elevation changes, water and forests (awesome in the fall).
Northwest Michigan (true Michigan golf!)
http://www.boyne.com/golf/golf_home.asp
http://michigan.twoguyswhogolf.com/northwest.html (reviews of everything up north)
Gaylord area (northern middle of the lower peninsula)
http://www.gaylordgolfmecca.com/course-directory-4/
Kalamazoo/Battle Creek
http://www.gulllakeview.com/home/index.php (multiple course complex)
http://www.heritageglengolf.com/golfcourse.htm
www.yarrowgolf.com
www.themedalist.com
Grand Rapids area
www.thousandoaksgolf.com
www.pilgrimsrun.com
www.cedarchasegolfclub.com/default.htm
www.thornapplepointe.com/
Near Indiana/Michigan border
www.golfwhittaker.com
www.lakemichiganhills.com
www.hawksheadlinks.com
Finally, these are the Best of the Best (IMHO). Pricey, but it doesn't get better than these. If you can play just one of these you will have a memorable round. Bring your 'A' game though!
http://www.arcadiabluffs.com/
www.bayharborgolf.com
http://www.grandtraverseresort.com/golf/the_bear.cfm
http://www.treetops.com/index.php?method=golf
http://www.forestdunesgolf.com/
www.stivesgolf.com