According to RVParks Review, there is a KOA and two other "RV Prks" in Van Horn. The others don't have very good write-ups, so it's pretty easy to connect the dots here.
As an alternative, Texas has a lot of good truck stops along I10 which is where I overnight while in-route. Also the rest areas are very nice, many even have wi-fi.. You have water, and restrooms which is more than you get at Walmart and if you just need a place to crash for a few hours, the truck stops work fine. I have no problem waking up, climbing in behind the wheel and driving for 20 minutes or so to find a cup of coffee.
Honestly, with Ft Stockton and El Paso within 100 miles on either side, I don't know why anyone would want to stop in that dust bowl anyway. To each his own I suppose. There are too many truck stops that welcome over-nighters because they know you are going to go in and buy something before you pull out.
2013 F250 XLT
I now have a Keystone Outback, but I try to help when I can.
Bitter Gun Owner