So I'm from San Antonio but working in Santa Teresa and while driving down 178 I see people shooting on what I assume in BLM land/public land. What is the legality of this? Can I go shoot as well? Is shooting an AR frowned upon?
Is there somewhere in the area I can go to shoot farther? Finally I've read up on getting a non resident permit for coyote hunting, is there a perticularly good place for this?

Thanks for any help, we don't have much public land in Texas and what is I'd be hesitant to use, plus it's quite the drive.

Basically all BLM land is open to target shooting in NM. You only have to follow state laws about where you can discharge weapons in relation to buildings/roads/etc. These should help:

http://www.blm.gov/nm/st/en/prog/recreation/recreation_activities/target_shooting.html
http://law.justia.com/codes/new-mexico/2011/chapter30/article7/section30-7-4

The one exception I know about is Bernalillo County bans all shooting everywhere that isn't a designated range. You won't need to worry about that down here in the free part of the state though

Castiel pretty much hit the nail on the head.

As far as your non resident coyote license, any sporting goods store (Walmart included) or online at NM Dept of fish and game dot com.

Thanks guys, I appreciate the help.