Boy, this is a tough question. There are so many nice places along the way and it really depends on how much time you have.
I'm with Lonny, Fredricksburg is one of the most memorable spots in Texas. We added an extra day to get through the museum there. San Antonio was also a fun place to visit. Houston, on the other hand, is an acquired taste. We would skip that if we did our last trip again. What other things you do on the way really are dictated by what you like. You can add Carlsbad Caverns which we did and it was wonderful. But, be aware that a lot of smaller town campgrounds in Northeast Texas and Carlsbad are filled with oil workers and you need to confirm availability in advance. Also, we found Natchitoches to be a delighful small town worth visiting. (It is sort of like a miniature French Quarter.) And, if you end up in Winslow, AZ, for the night be sure to go to the train station and have dinner in the Turquoise Room. (You can thank me later.) We also opted to stay in Breaux Bridge, LA, versus Lafayette. It is a cute town.
As, you can see, these places are all spread out and picking a route is no easy task. But, it is a fun trip and worth the journey.