where to shoot in new mexico?

i live in texas, and just happen to have stumbled on a week with absolutely zero responsibilities. in my home state, pretty much all land is private, and shooting requires access to a a friends ranch, or some sort of official shooting club. i recently picked up a 7mm rem mag, and its doing good enough at 200 that i feel like i can take it out far. so, i know that in new mexico and arizona, there is blm land that you can shoot on with minimal restriction. the problem im having, is how do i know if im in an area thats a-ok? dp any of my long range brethren in new mexico know any specific places i can set up, or can help me figure out how to find somewhere? id like to get a mile, but really, anything over 1k is further than i have access to here.