Wilderness campground is a state park, about $30 a night with electrical hook-up is south west of the bridge. Straits State park is just across the bridge to the east and features beautiful bridge views. Electrical hook-ups as well. We are currently at Mill Creek campground, privately run, about 3 miles south east of the bridge, varying hook-ups and more expensive but very nice for the kids. Any will work well fir you. There is also a KOA just outside of Mackinaw City.
In order to request a driver across the bridge there is a place to stop just off exit 338, either an MDOT or Bridge Authority office. Have fun!