Another good place for overnighting in the El Paso area is at Cattlemans Steakhouse outside of Fabens (I-10 Exit 49), North about 5 miles on TX 793. The restaurant is located on the Indian Cliffs Ranch (a working ranch) and you can dry camp for free in the upper parking lot. We have camped there numerous times over the past 20 years, last time in 2015. Enjoy a meal in the restaurant (which sits on a bluff) in the evening and watch the lights come on in El Paso, 25 miles away. Road up to the restaurant from TX 793 is a bit steep but we have seen all sizes of RVs in the parking lot over the years. 1st time we stayed there we were driving a 39' DP with a toad.
Best steaks anywhere at reasonable prices.
See http://www.cattlemansranch.com/ for more info and menu.