Michigan/Wisconsin/Minnesota best time

Having lived in the U.P. I'd be more inclined to go in late August to mid-September. I've seen it snow in the western U.P. in mid-September. You can go later than that, but if you want decent weather go earlier than mid-September.

Also, the campgrounds won't be crowded in late August, although there will be more campers Labor Day weekend, but not to the point you can't find a campsite.