Unless you have a reason to head to Columbus consider doing the 81 to 40 way. There is so much to see it's impossible to do it all. Ever been to the Biltmore House in Asheville? It would be easy to drop down to Asheville from 81 and pick up 40 there. Then you have Pigeon Forge/Gatlinburg if you want. Then Nashville and Broadway street and the Hermitage. Oklahoma has a few things to see.
In Amarillo there is the Palo Duro Canyon as mentioned and the Big Texan Steak Ranch. Good steaks. New Mexico has a few things to see. Williams AZ is the town to stay in and DO take the train trip up to the Grand Canyon. The RV park is right there where you get the train and it has a wonderful buffet restaurant for breakfast before you go. We stayed there some years back and it was a great park then. Williams is on route 66 and it has that historical theme.
What I have done in the past is gone online and ordered the travel guides from all the states we were going to pass through. Very helpful to have the hard copy in hand when planning. Is there a return trip planned? Do the northern route back and go see Mt. Rushmore.