We took our kids to the following places when they were early teens. Now, as adults, they still want to return often.
Consider Badlands NP near Rapid City SD, where the kids can run and scramble over various rocks and along paths. Nearby is Mt. Rainier NM and the Crazyhorse monument. Also, reasonably close is Devil's Tower NM (the monolith in Close Encounters ...). Hike around the base and learn about the Indian legends. From there you can drive to Cody, WY and see the Buffalo Bill Museum (first-rate IMHO) and the Irma Hotel. Maybe take in a rodeo. Then, just two hours to Yellowstone NP eastern entrance. After Yellowstone, head south to Grand Teton NP. Consider tubing down the Snake River and/or taking a boat ride across Jenny Lake (?), and a short hike to Hidden Falls. Look for Moose and other animals. Enjoy the "gunfights" in Jackson WY, and see the town square made famous in Clint Eastwood's "Every which Way ...".
Have a great trip with your family.
Bob
