When we stayed on the banks of Lake Superior we were at the city campground in Grand Marais, Michigan: Woodland Park.
https://www.burttownship.com/recreat...rk-campground/
If you're going to do a UP tour a stop in Houghton, Michigan can be fun and their city park is also quite convienient being right downtown:
https://www.cityofhoughton.com/rv-park/
Going South you may want to stay near Mackinac Island (of course you can't camp there you have to stay in either St Ignace in the UP or Mackinaw City in the LP). Mackinaw Mill Creek has some spots available on the beach but it is a huge resort type family friendly campground:
https://www.campmackinaw.com/
Finally, one of our favorite campgrounds is an Ontario Provencial Park (granted its a bit of a pain going there for now and I think they are closing down for the season soon but still): The Pinery Provencial Park on the shore of Lake Huron is a great spot for a long weekend.
Welcome to Pinery Provincial Park