OK some thoughts on that route -- once I say that I'd be headed the other way in July!!!
Here we go: I-25 to Raton. There is a great little park at the top of the pass, but probably too close to your starting point for overnight there.
At Raton take US 87 across NM to Clayton and on to Amarillo. A nice stop in July would be at Palo Duro Canyon (state park and other parks nearby). The outdoor drama "Texas" will be playing in the park.
Back to Amarillo and US 287 to Wichita Falls. Of course you could stay on 287 on into Fort Worth, but another possibility is to take US 281 out of Wichita Falls. Many possible routes from there. I'll mention one possibility: Texas 6 to Waco. A really nice COE park (Airport Park) at Waco and the tourist destination of "Magnolia" by fixer uppers, Chip and Joann. Also the Texas Ranger Museum and Baylor University. You could take TX 6 on down to TX 36 and entirely bypass Houston. TX 6 will bring you to Bryan/College Station and Texas A&M and the George Bush Presidential Library.
At Hempstead you will intersect with US 290 which will take you on to Houston or you can pick up TX 99 and bypass Houston to pick up 6 again all the way to Galveston.
There are many, many variations on this route, but at least I have sketched out one.
