I'm sure you know all the major things to see. My suggestions are for the sites not so well known, but still important. In the Western states consider:
In South Dakota:
1. I90, exit 131 is the HQ for the Minuteman Missile NHS. Go to Minuteman Missile National Historic Site (U.S. National Park Service)
and read about it. Reservations are a must.
2. I90, exit 131 Prairie Homestead. Go to Badlands, South Dakota Attraction - Prairie Homestead
and read about it.
3. I90, exit 131 Badlands NP, go through the Badlands and exit the park via the South entrance. A couple of mile from the south entrance is the Badlands KOA. Go to https://koa.com/campgrounds/badlands/reserve/
for details. I suggest this CG because it is easy to spend a day at the NP and then the evening at the amphitheater to view the sky. At the south entrance to the NP there is an amphitheater. Go to the amphitheater at sunset. About 90 minutes after sunset it will be so dark you can not see your hand in front of your face. This is important because once your eyes get used to the darkness the sky will be full of stars. I do mean full. There is no other place I have ever been where the night sky has very little black. There are just too many stars. One can see the Milky Way Galaxy, planets, Russian satellites keeping a watch on our missiles. Touring the Badlands one can stay on the main road loop and see (short hikes) more than one would expect.
4. Wall Drug - At the western end of the badlands. Go to walldrug.com
and read about it. It is a tourist stop. The best buffalo burgers are served here. The kids will like all the tourist stuff they can buy. This is one of those must stops. Once in the area, everyone will ask if you stopped at Wall Drug.
5. Mammoth Site, Hot Spring, SD. This is an active archeology site. All indoors and HVAC controlled. Go to Welcome to The Mammoth Site in Hot Springs, South Dakota
and read about it. The kids will really like this stop.
In Wyoming consider:
6. If you're going to Billings on the way is Devils Tower (Devils Tower National Monument (U.S. National Park Service)
) and the Little Big Horn Battlefield. ( Little Bighorn Battlefield National Monument (U.S. National Park Service)
). There is a little known NHS called The Medicine Wheel NHS (I90 exit 9 in Wyoming). Go to http://www.medicinewheel.com/
and about it. If you go, leave the RV at an I90 CG. Do not take it on Rt 14. Pack a lunch or eat at the restaurant where RT 14 and RT 14A split. The Medicine Wheel is at 10K' above sea level. From the ranger station is is 1 1/2 mile walk to the site. I've been there many times (in the summer) and always encountered snow. Take warm clothes.
In Utah consider:
7. Salt Lack City area - The site to see is Antelope Island. One can swim in the Great Salt Lake. There are several beaches and eating facilities. There is also a 23% grade that is fun to go up then down (in the car, not the RV). Go to http://www.utah.com/stateparks/antelope_island.htm
and read about it.
In Colorado consider:
8. Forgetting about Denver. Instead go to the Estes Park area and spend some time in Rocky Mountain National Park (RMNP).
9. Pikes Peak - Nice day trip for the car. Leave the RV at the CG. Drive up to the top. Let the kids play on big boulders at 14K'+ above sea level. On a clear day it is quite a view.
10. Royal Gorge + Bridge - West of Pueblo Walk over the bridge. It is quite a way down.
In the East consider:
11. Asheville, NC is very expensive. Instead consider the Gatlinburg, Pigeon Forge, Sevierville, Tennessee area. There is quite a bit of entertainment, many CGs and the Great Smoky Mountain NP (GSMNP) is a few miles away. If you go to GSMNP, Clingmans Dome is a must stop.