Hey Jersey, Michigan has some great state parks. The West Coast of Michigan along Lake Michigan is wonderful with places like Saugatuck, Holland, Muskegon, Grand Haven, Petosky, and others worth visiting. There are state parks following up the coast, usually with 30A electric only. Going this way will take you almost right into Traverse City. You want to plan a few days here at Traverse City State Park which is huge, 300 + sites. There is a walking bridge over the highway to a beautiful sandy beach on Lake Michigan. Downtown Traverse City is only 3 miles away. This area is also near Sleeping Bear Dunes National Seashore. Well worth the visit for a day. From TC you would also want to plan a day trip up the Leeland Penisula taking you to waterfront towns, fresh catch seafood, wineries, and other delights.
Going up the East Coast, probably easier coming from NJ plan a stop at Sterling SP, in the town of Monroe. This CG is located on the shores of Lake Erie with views of the lake. They have FHU sites and 30A. I stayed there this past September to head to the Ford Museum. Even though it is about a 30-minute drive to Dearborn and the Museum it's a quick ride on I75. If you go to the museum plan on at least two days to see it all. From here motor up I75 to Frankenmuth Michigan. This authentic Bavarian Village is worth a day or two visit. Before our stay at Sterling SP, we were in Frankenmuth for Octoborfest (a blast). Great private campground with 90% pull-thru FHU sites is less than 3 miles from town, Pine Ridge Campground, about $56 nightly. We've stayed here a couple of times. From Frankenmuth head back up I75 to Bay City, MI. Great small city with Bay City SP one of the better SPs we have stayed at. From here you can head over to Traverse City, there probably are more state parks along the lake shore if you check it out.
In Mackinaw City, try to get a site at Wilderness SP, right on the shore of Lake Michigan. A Great CG! only 6 miles from downtown Mackinaw City and the ferries to Mackinaw Island. If you travel with your own bikes, for an extra fee you can take them with you to Mackinaw Island.
Hope this helps, Michigan is one of our favorite states to RV in, a lot of great state parks and places to go and see.