Michigan Recreation Search
Mostly I use state rec areas for camping. Hopefully the link shows you a map where you can filter down to just camp sites.
The great thing about the state rec area sites is, if you show up late in the day "under your own power" and the campground if full, they have to give you a spot, as you don't have time to get somewhere else.
At least that's what I have heard!
https://groups.google.com/forum/#!to...ng/82q7lqhLnz0
I'm going to peruse the links others have offered. Cheers.