Pigeon River Country State Forest [1] (off Sturgeon Valley Rd., 989/983-4101, $15) offers 29 rustic sites in a nice secluded setting. For waterfront sites, try Otsego Lake State Park [2] (7136 Old 27 S, 989/732-5485, state park vehicle permit required, $16–26) with 206 sites on or near Otsego Lake.
Links:
[1] http://www.moon.com/destinations/michigan/northeast-michigan/gaylord-area/pigeon-river-country-state-forest
[2] http://www.moon.com/destinations/michigan/northeast-michigan/gaylord-area/sights/otsego-lake-state-park