Go to michigan.gov/dnr and that website will give you all the hunting/fishing regulations, some downloadable maps, etc. Good place to start to get a feel for what time of year you might want to come.
Fall colors are usually peaked around the first part of October, nice time to be in the woods grouse and wookcock hunting.
Deer bow season runs from Oct 1st thru Nov 14th and Dec 1st thru Jan 1st. Rifle deer season is Nov 15th thru 30th. In normal years expect at least some snow during the rifle season, with more up towards Lake Superior and less (or sometimes none) in the southern parts.
In July and August temps can be 90 degrees, but not very often. More average highs are usually closer to 75 or 80. In early October I've hunted grouse in a T-shirt some days and other days you might need longjohns and an insulated jacket!
Walleye and Pike seasons open May 15th. Also available are perch, bluegill, crappie, brook and brown trout, and bass in the inland lakes/rivers. Lots of charter boat fishing for Lake trout, rainbows, and salmon on the Great lakes (Superior and Michigan).