Bakers Hole Campground We spent 2 nights there in June and three nights over the 4th of July weekend. Nice place with some sites adjacent to the Madison River.
We also used Rainbow Point Campground about 4-5 miles further from West Yellowstone on two occasions because Baker's Hole was full both times when we got there late in the day. Only downside to Rainbow Point was that there is about 2 miles of washboard road going in.
Both of the above are good locations for touring the lower loop of Yellowstone.
We also used
Colter Campground just beyond Cooke City for three nights to visit the Lamar Valley and Tower/Roosevelt areas in the northeast portions of the Park. Nice campground with great mountain views. Good location for driving the Beartooth and/or the Chief Joseph Highways.