Sorry to be slow. As others have pointed out, the State Park is the closest camping. It'd be great if they'd allow it on the hotel site, but it's against their zoning (I looked into this).
The Photostock Website has links to the State Park and other options for lodging. Here's the link to that page as well as a direct link to Petoskey State Park reservations.
Petoskey State Park
Hope to see you there!