We did a similar two-month trip from the east coast with a motorhome in mid-August to October 2013 - I definitely recommend it!
We met up later with friends who flew to the Black Hills, rented car, and drove to Yellowstone. We realized after talking to them that we saw so much more, there was just no comparison. If you have the time and the RV, this can be a trip you’ll never forget.
Some highlights:
Followed part of the Lewis & Clark Trail, camped along the Corps of Discovery route, stopped at numerous markers and museums including the great one at the St. Louis Arch.
A week in the Black Hills of South Dakota at Custer State Park - many area things to see.
A couple of days in Cody, definitely! Yellowstone (we camped at Fishing Bridge), and Grand Teton (at Colter Bay RV Park), Both CGs are inside the parks and have electric hookups.
Headed south to some great places - Dinosaur National Monument, Colorado National Monument, Black Canyon of the Gunnison, Ouray Colorado, then drove down to New Mexico.
Anasazi Heritage Center, Canyon of the Ancients, Hovenweep National Monument, Aztec Ruins NM, Chaco Culture National Historical Park. Had a fun day riding the Cumbres & Toltec Scenic Railroad.
Taos was a highlight including the High Road. We camped at a very low cost at Riana Abiquiu Lake Campground (Army COE.) Visited Georgia O’Keefe’s home and Ghost Ranch where she painted. Went down to Santa Fe, one of my favorite places in the West, Toured the Bradbury Science Museum at Los Alamos.
Grand finale - the Albuquerque Balloon Fiesta. What a trip. Loved every minute of it.
Just an example of all that’s available in our big country to see once you hit the road. Even if you come straight across from the north both ways and ignore the Colorado and New Mexico parts we enjoyed, I think you’d have a wonderful trip!