I have hunted NM as a non-res and understand. There is a map that shows private land in white and public in green and I think it's a BLM map. It is a real checkerboard and you need to be very careful to study and understand boundaries but there is a lot of good public hunting land. Watch out for jerk outfitters(not all outfitters) who will try to tell you public land is private to get rid of you. Keep the map on you at all times so you can stand your ground if this happens. Good hunting.