We camp in that area all the time. There are a few KOA's that would be close. Gaylord KOA would be about an hour drive to Mack, just stayed there a couple weeks ago. Grayling has a Jellystone (altho it's a bit more than an hour to mack, it is straight up the highway)
there is a Jellystone in Indian River, which is quite close.
The state park with full hookups is Hartwick Pines. That is a very popular park, so usually quite full.
Take a look at
that's at least a starting place.
Also, if you don't have to have water at the site, Wilderness State Park is great and is just outside Mackinaw City. Just across the straits is St. Ignace state park, right on the water looking at the bridge.