there is a lot if you are not going to be in a rush and not tied to I10. A few have been noted already, also have the Kings ranch in south texas to look at, NO??, only thing I would go back there for is the battle site of NO's. Took the boat tour to it but was too short on time to really look at it. NO itself, no big deal, typical tourist trap. In texas go to marble falls not far off I10 in austin area, not much in west texas along I10, Van Horne KOA is pretty good, gives mil discount as well. Just nothing in Van Horne! El Paso check out the roads to white sands, go to mex if brave enough. In NM again cn go to white sands missle range and the white sands NM. Over further in NM can go down to columbus and tour pancho villa raid area. rodeo NM buy some fresh Honey. sop at sterns thats where the area is for sinatras dirty dingus movie, wilcox az have apple annies, fresh pies and pick own fruit! Go down 191 to the chiracaua NM, about 50 miles off I10, take silver route to west and see Ft Huachuca, also over by Bowie you can actually go to Ft bowie see apache pass and old wells fargo route. in Tucson, can stop at the AF bone yard for a tour, visit the air museum.
There is a lot to see just have to look for some of it. Oh yes in NM/tex can go to carlsbad caverns in guadelupe mts.
Once in the east LA area, will depend on where you plan to set up camp on where you will want to go.