Campground suggestions in MIchigan

We only camp in state parks and have been to most of them in Michigan (lower peninsula). Most parks only have electricity and you have to fill your fresh tank at the dump station upon arrival. A few campgrounds have only a couple full hook ups. You can't go wrong with any state park along Lake Michigan. We like Ludington state park but it can be hard to get into, but probably not in September after school starts.

https://www.midnrreservations.com/

For Pictured Rocks, we stayed at a CG named (something like) Wagon Wheels - private CG, lots of trees. We had a popup then, so didn't care much about overhanging branches, so I can't address that issue. I have since seen pictures of the Munising city/county campground and it looks wonderful! Lots of folks here seem to recommend it. Both have at least some hookups.

We stayed at the St. Ignace KOA, again with a PUP, and liked it well enough. Straits State Park would also be a good choice - it's in St. Ignace as well. No water hookups to my knowledge but they do have electric; I'd really recommend reservations. We have stayed at Mackinaw Mill Creek CG, which many recommend, but it was huge and we HATED the FHU sites we were in at the time (which was over 25 years ago).

We did a day trip to Sleeping Bear Dunes from the Petoskey KOA, where we stayed. Nice CG but not as wooded as we would have liked.