From I-80 in Wyoming I'd recommend exiting at Rock Springs, WY to Hwy 191 which will take you into Jackson, WY. Continue north through Jackson into Grand Teton Nat'l Park - a MUST stop. It's altogether different than Yellowstone in looks and things to do. If you want hookups, stay at Colter Bay RV in the park. If you want dry camping, stay at either Gros Ventre campground or Colter Bay campground (next to the RV park) which are both in the park. The two dry campgrounds don't accept reservations but they have 300 sites each and rarely fill even mid-summer. You won't have a problem getting a site. The RV park accepts reservations.
From Grand Teton Nat'l Park just continue north through the park and the road continues into Yellowstone Nat'l Park. It's all an easy drive with an RV.
Each park has an awesome web site which gives you driving, camping and things to do information. Read them thoroughly. They're very helpful.
Grand Teton National ParkYellowstone National ParkHave everyone bring very warm clothes for the end of May - coats or layers and even hats and gloves. It could be very nice but then again, you could have some cold temps.
Full-Timed for 16 Years
.... Back in S&B Again
Traveled 8 yr in a 40' 2004 Newmar Dutch Star Motorhome
& 8 yr in a 33' Travel Supreme 5th Wheel