West Yellowstone, MT has many RV Parks with varied prices. Never been there mind you, but have read may reports & suggestions from folks who have been.
Gardiner, MT just at the
North Entrance by Mammoth has a few RV Parks. We have been there, but not in a RV Park.
Cody, WY would be the most east entrance with not only
Several RV Parks in the Cody area. But one would have a longer drive into Yellowstone from there.
South Entrance is near
Jackson, WY & the Tetons.
Here's an Old Post on
Yellowstone & Wyoming Sites & Sights, maybe something in it will be of help.