We have been there three times, love that place.
We prefer the spring the best, over Memorial Weekend.
We have stayed inside and outside the park. We like Grizzly RV Park in West Yellowstone the best. Close to the West Entrance and also can go downtown for meals if you don't feel like cooking.
Get yourself a Golden Age Pass,(age 62) either on-line ($20.00) or the first day you enter the park ($10.00) This pass is good for all the National Parks forever. It also will give you discounts on SOME camping in the NP.
Highway 20 from Idaho Falls to West Yellowstone is fine for RV's.
Check my blog for pictures. Year 2013