If you don't mind USFS campgrounds here are a few places you could look into.
There are lot's of campgrounds in the Black Hills, just find something you like and don't go during Sturgis.
It looks like you may be stopping at Devils Tower, there are both Forest Service campgrounds and a KOA.
There are a few USFS campgrounds between Buffalo and Ten Sleep along 16.
A number of campground in Cody that I have stayed at, one on the SE side of town and one West of town.
Fishing Bridge in the park. Grizzly RV park in West Yellowstone is nice.
Slightly out of your way but you can take Mt 1 at Anaconda, it is just a scenic route off of I-90. There is a very nice USFS campground on Georgetown Lake that even has electricity to some of the sites.
Apgar at Glacier.
After that the only place I have camped was Billings,
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