Not much nearby worth a special trip. You will probably be driving through a nice part of Arkansas and Eastern Oklahoma that is worth a stop. Palo Duro is pretty isolated unless you want to explore Amarillo and The Big Texan for some rocky mountain oysters. Also, I can't think of his name, but there is a football and basketball coach on the board here who lives just outside Amarillo in a town called Groom. He may have more.
If you are willing to expand the radius you are probably 4 hours from Monahans dunes where you can go sandboarding. Carlsbad caverns is close to Monahans. You are probably another 5 hours from Taos which is cool too...
We hit Palo Duro on the way to or from Colorado, AZ, or New Mexico for a day or two. It's cool, but not much else close by so we keep trucking.