I have always preferred the amenities of private campgrounds, so I will offer some of my favorites along your travel route:
West Yellowstone KOA, yes a KOA. A real resort type campground, indoor heated pool, premium sites have full concrete pads and patios, lovely patio tables and a private adult swing. Really nice park.
In Jackson, Wy, we like The Virginian. Not much of an RV park, clean, adjacent to a hotel with hotel privileges, but a perfect location for touring Jackson.
If you get to Durango, CO, Aspen Rose is delightful.
Monument Valley is worth the trip, and Gouldings RV is the only game in town, very nice, but distant to everything except Monument Valley.
South Grand Canyon I recommend basecamping in Williams AZ. The Circle of Pines KOA is great, big trees, indoor heated pool, very large sites, dirt, but well maintained.
Just some ideas, Happy Trails.
