Sleeping Bear Dunes National Lakeshore camping

You could also try Interlochen State Park. It's a bit of a drive (30 miles) to Sleeping Bear but you can almost always get a site. There is also the advantage of proximity, right across the road, to the famed Interlochen Music Camp. There are scheduled concerts, both free and paid, and if the camp is in session you can walk, wander the campus and enjoy the music from the supremely talented young people in attendance.