if you want hookups, Fishing Bridge in Yellowstone and Colter Bay RV in the Tetons are your only options for staying inside the parks.
West Yellowstone, MT has several rv parks and is right on the border of Yellowstone.
If you can live without hookups, you can do Mammoth or Bridge Bay...if you can get reservations. they have sites big enough but not many of them.
For the Tetons, we like staying down at Gros Ventre campground, with water and a dump station, 7 miles from Jackson, 3/4 miles from the park. But you can find a decent rv park in town. The Virginian looks good from the street and is on a tourist bus route.