Because of the snow this year, I'd head west using a southerly route. Consider taking in places like Santa Fe (Bandelier NM), Chaco Canyon, Mesa Verde (Durango), Hovenweep, then up to the Moab area for Canyonlands and Arches. Continue north through Vernal to see Dinosaur NM and the Utah Field House in Vernal (great museum). All of these places should be good to go by the time you get there in early to mid-May.
Head into Grand Teton from the south and spend some time until your reservations in West Yellowstone. They're aiming to get the south entrance road opened around May 10.
After Yellowstone, begin a meandering path up to Glacier NP, maybe venturing into Idaho also. Craters of the Moon, Sawtooth Rec Area, Bitterroots, etc. there's lots of options there.
To best see Glacier, I'd recommend spending a few days on each side of the park. You'll have to take US 2 around the south end as you can't take you rig over Going to the Sun Road.
On the way back east, catch the Black Hills, Custer SP, Mt. Rushmore, etc. If you haven't been, NW Arkanasa and SW Missouri have interesting scenery, caves, etc.
I also echo those above and encourage you to use your water and holding tanks so you can expand where you can stay. Also, check into state parks along the way as they often have flush toilets and showers even if they don't have FHU. And in many of the mountainous places in the west like Grand Tetons, Yellowstone, Glacier, etc., you won't need electricity for a/c as it just doesn't get that hot.
Ken & Allison
2 Camping Cats (1 diabetic)
1996 4Runner, TRD Supercharger, Edelbrock headers
2007 Fleetwood Arcadia, Honda EU2000i
4 mountain bikes, 1 canoe, 4 tents, 8 sleeping bags, 2 backpacks
(You get the idea!)