We found some interesting spots in your area. In Chattanooga the aquarium is a very interesting place, and great for the kids, in addition to the tram to Lookout Mt. Also, in Southern Tennessee is the Shilo Battlefield, which is a very interesting historical venue. Yellowstone is very interesting, and quite time consuming if you take time to visit all of its features. As you go South from there, the Air Force museum at Ogden, Ut. is quite interesting, free, and entertaining. The National Parks in Utah are numerous and quite beautiful. Arches (East), Bryce Canyon (Central) and Zion are all beautiful places to see. I also recommend, that if you are going South, take time to drive into and visit the north rim of the Grand Canyon, which we found to be more spectacular than the south rim.
There are so many things to see that it is almost impossible to see them all in a limited amount of time. Hope you enjoy your trip.