It's been over 4 years since we camped at Yellowstone...had an easier to maneuver 24' Class C and no tow car at the time.
Stayed at Fishing Bridge (inside the park) in a pre- Memorial Day timeframe. Full-hook-ups and fire-rings/picnic tables... not sure if things have changed since then.
We plan to re-visit, again at off-season. Have targeted Cody, Wyoming for base camp, drive the Element around for day trip explorations. (Better fuel economy...ha!)