Red Lodge. A nice KOA west of town, never camped there, but looks nice and there used to be someone on this site who was a camp host there.
Also plenty of FS campgrounds if you don't mind dry camping.
It is also the start of the Beartooth Parkway that leads into the Northeaster entrance to Yellowstone NP, or you can cut off to the Chief Joseph Parkway that heads to Cody and circle back to Red Lodge. Makes a great one day trip.
And some fantastic scenery....
If going over the 4th, the NPs will be extremely busy, as will most of the area. So get your route planned and make some reservations.