Farmer Bob, if interested in RV parks outside of the Nat'l Park.
West Yellowstone, MT has many RV Parks with varied prices. One should be able to find a rental unit there as well. 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. Not sure if one could find a rent car there. But Livingston, MT is about 54 miles away. Might find one there.
:C:C Cody, WY would be the most east entrance with not only
Several RV Parks in the Cody area, with several rental car sites in Cody. Even a state park is near. But one would have a longer drive into Yellowstone from there.
South Entrance is near
Jackson, WY & the Tetons. I'm sure there will be rental cars sites there as well.
Here's an Old Post on
Yellowstone & Wyoming Sites & Sights, maybe something in it will be of help.