...My mother was from Amarillo in the Texas Panhandle. I still remember visiting Palo Duro Canyon State Park as kid long ago. Really spectacular. http://www.palodurocanyon.com/
Worth a visit...
So were you the kid in the suspender shorts by the blue '59 Desoto at the scenic overlook? ;-) I spent lots of time there as a kid in the late '50s, early '60s, too, having spent the first 7 years of life in Amarillo right by the Pantex Plant absorbing all that radiation.
Since it's Texas, which is a "whole 'nother country" (and proud of it) Palo Duro is half the distance of a large European country away from I-35 and the OKC to Houston route.
I made that trip from OKC to Houston just six months ago for a funeral. I'd lived in the metro-OKC area for 35 years but been away for 10. I thought I'd stop and visit all my old haunts. My first stop was going to be a visit with an old friend who dealt in Jaguar & Rolls, with an ulterior motive of using his executive washroom. When I got to the highway junction where his dealership had been, there was now a humongous Native American casino. Then the place where I had lunch nearly daily was a different building with a different menu, though still a restaurant. Every other place I used to frequent had changed as well. (Even the cemetery where 5 generations of my family are buried had been moved a quarter mile north from where it had when I got there!)
Stopped to see my old house of 30 years and found it's now the color I'd always insisted to the Historical Commission that it *should* be, but which they'd always nixed. At least it and my favorite neighbors were still there so I hadn't wandered into an alternate universe.
There'd only been one place I ever suggested people stop passing through that way--an old cafe established around 1910 by the trainstation that'd evolved into a great micro-brewpub where I spent every Friday evening for more than 30 years, having two glasses of the best stout ever over a good dinner. But it burned to the ground four weeks ago, so I'm left with no recommendations for stops.
If you want to see the remains of the oldest mountain range in North America, without getting much off the Interstate, the Arbuckle Mountains just north of the Oklahoma-Texas border are quite beautiful. Of course, being the oldest, they're the most worn down and smallest still called "mountains". But what I find so beautiful about that area is all the craggy layers of exposed and upheaved ancient rock along the faultline where the mountains once stood. The scenic turnout is right off the highway so it adds very little time to the trip to drive through and see some of the oldest geological features on the continent. Even if you skip the turnout, you get several miles through the cut that was made for the interstate in the mountains. I've always wanted to build my last ultimate house there.
Palo Duro is beautiful, but I doubt you'd want to drive that far, especially across the desolate high plains between you and it, to see it. Heck, I wanted to see it again after all these years and even I didn't want to drive the mere 50 miles south of the interstate across yet more high plains after driving from LA and through Amarillo.
Fort Worth has several fine art galleries and San Antonio is well worth a stop for some lovely old hotels/restaurants. Houston? Most people don't like to drive around it because of the traffic on the loops. My view is the only way to do Houston is to stay on those loops and drive *around* it. (My sister lived there for many years and she loved it, so what do I know? We still argue that point.)
It's good big country and good people out here but if you stay along the interstate corridor it won't look much different near any metro area from the interstate in LA, except there won't be palm trees and all the interesting bits will be some hours off the main go and taken for granted by the locals such that they won't even be marked.
Just don't eat at that hamburger stand 40 miles from nowhere in the Arbuckles unless you've got a colonoscopy scheduled the next day.
I hope you enjoy your visit.