We're in MI as well. Our kids are younger at 11, 9, and 5 and all have grown up camping either in a tent or in the TT purchased 3 years ago.
Hartwick Pines in Grayling was an excellent state campground. Very clean and some sites were large. We all really enjoyed going into the forest and the logging museum. We went on a ranger led tour as well. It had a nice and short hiking trail to a small fishing lake. There is no pool or swimming lake/river, so it's best in the spring or fall. Bring bug spray for the forest in the spring.
Tawas Point State Park is another one of our favorites. You can get a site right on the bay side of the lake and walk through a tree line from your site to the water. They also have a dog beach, lighthouse tours, and you can walk to the large beach with the open water and bigger waves. They also had a free ranger led program for fishing a nature walks.
Ludington State Park was just an amazing place to visit, but the sites are absolutely awful and it's practically impossible to get into. Maybe stay in the local area and go into the state park to visit. That's what we'll do next time we want to go there.
Last summer we went to the Yogi Bear in Fremont Indiana, it's just over the state line. It is a BUSY place and on the freeway.....you don't go there for peace and quiet but my kids loved this place and want to go back. It has 4 pools and 3 water slides and they rent out golf carts.
The only place that I really wouldn't recommend is Traverse City State Park. Horrible beach, the area is super crowded and in the middle of the city. You can drive to the Sleeping Bear Dunes, which is a nice visit but I'd stay someplace else to visit the dunes.
For longer trips we've gone to the UP for Tahquamenon Falls, Pictured Rocks, etc. We've also been to Mammoth Caves in Kentucky. I'd recommend both of these as well.
Have fun. Glad to hear that the teenager is looking forward to it. FYI, book your sites early, especially for those that are on a lake or holiday weekend.
2017 Coachmen Catalina 323 BHDSCK
2018 Ford F150 FX4
3 growing kids and 1 big dog