Which way are you coming from and what do you prefer? From the south, it is best to stay at one of the parks around Mackinaw City, from the west around St Ignace. Looking at 30 miles out from the ferry docks, you will find state park and RV park options on both sides of the bridge, and State Forest and National Forest campgrounds on the north side.
If you don't want to drive to the docks, on both sides you will find at least one commercial RV park within bicycling distance of the ferry, and as AFAIK the ferries still carry the bikes no charge. You'll use them to get around the island, save yourself the rental fee and have a bike you know fits your body. Tiki RV Park is close to the St Ignace docks, Mackinaw City KOA to the Mackinaw City docks.
I can't recommend any RV park specifically, as I visit one of two other ways.
For a day trip when RVing, I'll do it passing through the area, usually coming from the west. I'll stay at one of the public campgrounds along the Lake Michigan shore, sometimes as far west as Manistique (Indian Lake SP), closest is a state forest campground (not RV park) on Little Brevort Lake, other state forest campgrounds further out.
My other way of visiting is a 2-3 night stay on the island, and for that I don't RV, rather I'll drive from Lansing or the Detroit area where I've been staying with family, and park at St Ignace.
What I won't do is stay 2-3 days off the island and commute by ferry every day. The relaxed experience of living on the island is just too much to give up.