Michigan is a big state, with lots of varied outdoor activities. The best parts in our opinion are up the coast along Lake Michigan, anywhere in the Upper Peninsula, and down the coast of Lake Huron.
Not knowing how much you want to travel each day is another difficult thing to tackle. Let me tell you the places I'd want to stop and you can go from there. Ludington, try (Poncho's Pond RV Park). Traverse City (Holiday Park Campground), Manistique (Manistique Lakeshore Campground), Munising (Pictured Rocks KOA), Newberry (Kritter's Northcountry Campground), Brimley, (Sunrise View RV Park), Alpena (Camper's Cove RV Park), Tawas (Oscoda/Tawas KOA), Port Huron (Port Huron KOA in KImball). If you want museums, you'll have to search locations by downloading the Pure Michigan Travel Guide. They won't be printing a new one until sometime in early 2022.
You also should know that weekends fill up real fast until the weather changes and even then people still head out weekends to see the fall colors. Also, be sure to cover the north as early as possible as you don't want to get caught further north when the early snow arrives.
Best of luck.