I would avoid the northern lower peninsula after about May 25th or so. Memorial day is pushing it. This in an average year. This year with still about a foot+ of snow, Gaylord area/North Central could push that back some. Have to see how the temp/precipitation patterns work out.
Mosquitoes are bad enough, but the black flies can be brutal. I sleep with no-seum level mesh unless the nighttime temps are 40* or below. The skeeters breed in the slow water, the flies in swifter, so with all the water sources in the state, it's really difficult to avoid one species or the other and almost always both.
Late May, all of June, and about 3 weeks of July best be avoided. August is better, September/October are great. Watch out for ticks anytime.