The West Siders used to go out to "The Wall" on Artcraft just over the New Mexico line, but they gated that off for now. I had thought it was BLM land, but they have some company in there doing land and gravel work. There's still some "secret" spots here and there out in the desert. You'll have to go out four-wheeling to find a place you like. I found me one down towards Santa T. A lot of old tires and such where some have made a makeshift shooting area.
El Paso is the best city in TX of course. Actually, my company closed in NJ and my girlfriend is going to medical school here. randmplumbing showed me a place in New Mexico this weekend.