In the Sleeping Bear Dunes area I would suggest Indigo Bluffs RV Park. Nice facility, closer to the dunes than Platte River, nice amenities. Most sites have water & electric, but there are some FHU sites.
http://www.indigobluffsrallypark.com/In the U.P. near Munising there is Munising Tourist Park just west of the town along M-28. The park is on the shores of Lake Superior with nice views of Grand Island.
http://munisingtouristpark.com/A bit further east of Munising is a very nice campground right in the small village of Grand Marais called Woodland Park. They don't take reservations, but you would have no trouble getting a site in September. The campground is on a bluff above Lake Superior and has water & electric hookups. You can walk into downtown. Check out the Lake Superior Brewing Co.
http://www.rvparklist.com/rvpark/1399/Read a bit about Woodland Park Campground at Rv Park Review.com below.
http://www.rvparkreviews.com/regions/Michigan/Grand_Marais.htmlIn the areas around the Mackinac Bridge Mill Creek is the go to place for most campers. We've never stayed there because we used to live about 55 miles from there and just made day trips to the island.
http://www.campmackinaw.com/