I will assume that you will be taking I-40 over to Nashville for the first leg of the trip. Stop in Nashville and go see the Hermitage, Andrew Jacksons home. Depending if you stay a couple of days there is Broadway Street to have fun on and the Grand Ole Opry to see a show if there is one while you are there.
Then I will assume you will head up to St. Louis. Of course, there is the Gateway Arch to see along with the museum below it. Lots of great craft breweries to visit. Then you can pick up 44 down to Springfield and see the first Bass Pro Shops store and the Wonders of wildlife museum. From there head down to Branson.
After Branson head back up to Springfield and take 44 over to 49 and then up to Kansas City. Pick up 70 into Denver. Never spent any time in either of those cities so can't tell you what to go see.
Certainly you can do some of your own research and see what may coincide with your interests. I usually go online and order travel guides from the states I will be traveling through. They tend to have area specific maps of points of interest. I find it nice to have the hard copy guides at hand while planning instead of spending hours online.
