Fort Stockton Walmart allowed overnight "camping" as of about a year ago. We moved ourselves from Houston to Tucson, and I slept there in the back seat of my truck 16 times. It is 24-hour.
Not too far out of your way is Tucson Mountain Park which has Gilbert Ray campground. Quiet, inexpensive, and very beautiful. No sewer at the sites, but has a dump station.
http://webcms.pima.gov/cms/one.aspx?portalId=169&pageId=1327
If your schedule allows, have dinner at El Capitan in Van Horn, Texas. Outstanding menu, creative chef, and wonderful staff. One night, I just said, "Gluten-free - surprise me," and was presented a fantastic meal. Worth stopping just to see the hotel.
http://hotelinvanhorn.com/
Should your schedule allow a couple of days in Tucson, PM me.
Matt B
oldMattB
1998 Monaco Windsor