Right around San Antonio NM there is BLM land surrounding the missile range. Go to the BLM office in ABQ (on Montano near 2nd) and pick up those quadrangels. The maps are 4bucks a piece and worth their weight in gold.
There are oryx in that area. you will need to do some scouting to find the best places.
Good luck. I apply every year, one day I'll get drawn.