My very favorite place to stay in Yellowstone is the Slough Creek campground. It's small, usually very quiet, and close to what I consider the best part of the Park (Lamar Valley area). Not too many other places in the lower 48 where you can see a bison meander by, hear a wolf howl, and catch two species of trout within a few feet of your doorstep. If the NPS didn't limit people to 10 (or maybe it's 7?) consecutive nights in a camp site, I'd be happy to just plunk down there in June and spend an entire summer.
"It don't mean a thing if it ain't got that swing"
- Duke Ellington