Consider this route through the eastern side of Arizona and part of NM when heading to Houston. I did the same part this summer when I was heading westward.
1) From Eagar, AZ, take highway 191 all the way down to Clifton. You'll go through Morenci, a massive open pit mine. great switchbacks. glorious road.
2) a little south of Morenci, take Hwy 78 eastward, then hwy 180 southeast to Tyrone. Then Hwy 152 to Caballo State Park. Riding through the Gila National Forest was one of the few times I would have willingly rode bitch to admire the scenery.
Once in Texas, Highway 90 from Alpine to Comstock is pretty scenic (for west texas scenery) and you can make great time too.