The island is nice but touristy. Worth a trip though.
Never stayed at these but it looks like they offer it. Busy season so make reservations.
Tee Pee Campground, Mackinaw City, MI, KOA, Mill Creek might too.
We tend to stay at Straits State Park over the bridge in St Ignace. No shuttle, but about a mile or so from the ferry. It's a nice town and great park.
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If you have bikes you are all set. Ride to ferry. The island is best seen via bike anyway (IMHO). You'll be very limited if just walking but there are bike rentals on the island.