Depending on how much time you want to spend in each place, please allow me to comment on Yellowstone.  Back in 2002, four of us chose to go there and then to Idaho to visit family on a two week vacation.  I figured that by just spending a couple of days in Yellowstone, we could choose to go other places as well.  Silly me....   I was informed that to really see Yellowstone, one needed to spend a lot more than just a couple of days.  We spent 5 days in the park, primarily hitting the places easily reached by vehicle with very little hiking to see some waterfall or other feature.  I've been told by the others that we pretty much saw almost all the major features, and maybe missed just one or two minor ones.

We managed to spend a fair bit of time in each place because I am a prolific photographer.  That was the early days of digital photography, and I took just over 1400 pictures in that 5 days.  Granted, that 5 days did include a few hours spent in the Grand Teton National Park.

If you are also making that circle to include the Grand Canyon, check out Utah's 5 national parks.  Zion, Bryce, Canyonlands, Arches, and Capitol Reef.  Check them in advance by looking for pictures online to see if any offer things you want to see.  Colorado's Rocky Mountain National Park is supposed to also be very good.

Good luck and have fun.

Terry

If you are planning to visit Mount Rushmore, I'd also add Custer State Park to your list of places to see in that area. We also enjoyed a visit to Badlands National Park.

I agree with Bill's suggestion to consider Glacier National Park as well if you are thinking about Yellowstone and Tetons. You won't be able to take your RV over the "Going to the Sun" Hwy in the park, so I'd suggest staying at least a couple of nights in East Glacier area and a couple of nights in West Glacier so you have time to visit different areas of the park.

Terry's comment on the size of Yellowstone is spot on, a very large park to see in a short amount of time. We broke our visit up into 2 different 4 night stays in 2 different areas of the park and then another 4 nights in Teton National Park. We left there looking forward to another visit, there's a lot to see and do in that park.

Craters of the Moon park in Idaho would be a fun stop for kids if you are heading south from Yellowstone to Utah or AZ, a very "other world" kind of experience.

Have fun planning.

And the DW just reminded me of Devil's Tower in Wyoming (think Close Encounter of the 3rd Kind).

Terry,

There is so much to see in the west that I'm pretty sure we aren't giving you all of the things to go see and do.  If you were to go through Colorado and Colorado Springs, for natural wonders, Garden of the Gods is a primo location to go.  One can take the cog railway up to the summit of Pike's Peak.  (If you had a regular vehicle, you could also drive up to the summit.  West of Colorado Springs on Highway 24 is a small town called Flourissant where there are huge petrified stumps.  If they aren't actually Redwoods, they are near the size of Redwood stumps.

If you go to SW Colorado, there is Mesa Verde if you are interested in ancient Indian culture and their habitat in the cliff dwellings.  Cortez, Colorado is about 115 miles from Moab, Utah, where the Arches National Park is located, and Canyonlands isn't that far from Moab.

Like I said, there is so much to see that you may wish you had 2 months.

Terry

North of Rawlins, Wyoming, on Highway 220 towards Casper is Indepence Rock Historical Site, where Oregon Trail pioneers stopped to get water and a lot of them carved their names and date of passage into the rock.

Barb

Way too much to do in a month. I would pick an area and concentrate on it. It's at least 5 days travel each way so that only leaves 20 days to explore. Yellowstone/Tetons/Rushmore/Devils Tower would be one option. Another would be the parks in Utah. Third option Colorado/Grand Canyon. Try to do too much and you'll only skim the surface and spend too much time traveling to and fro. If it was me I would do Utah again and we've been most of the places mentioned so far. 

Depending what time of the year you are headed into Glacier National Park (Waterton borders Glacier = National Peace Parks), there is a shuttle bus that can take you on the going to the sun road with stop offs, this is far more relaxing and enjoyable to view than white knuckling it even in a car for some as many reviews mention.

Flathead Lake (we camp here a couple of nights), Whitefish, Kalispell are some of our favourite stop offs for an hour or two here and there.

Garden of the Gods Colorado our party of 7 loved the horse riding in = maybe a surprise for your grandchildren???