You also might consider Flagg Ranch (Officially now Headwaters Lodge). The sites are a little close together (we have not stayed at the Coulter Bay RV Park so I can't provide a comparison), but you are in the trees and generally have good shade. The RV sites are full hookup. There are some tent sites mixed in with the RV sites. We had a tent site next door and one of the three occupants that were there when we were weren't too happy about it. Also no cell service in the campground. Some wifi in the lodge. At Coulter Bay you can get a signal, but its spotty.
The "lodge" is basically only a front desk/tour sales desk, gift shop, small store, gas station and a fairly nice restaurant. It about 15 miles north of Coulter Bay (2 miles south of the south Yellowstone entrance). Not as high traffic area as Coulter Bay.
We stayed in a non-hookup site in the Coulter Bay main campground a couple of years ago. They do have some electric sites, but those are hard to come by. We checked in at 10:00 and the electric sites were all gone (main campground doesn't take reservations).
There are also a couple of commercial RV Parks near Teton. We passed Fireside RV park about 4-5 miles east of Moran Junction on Highway 26. Looked "OK" but its on the Prarie and doesn't have much, if any shade. We haven't stayed there, so I can't provide any better information
