I like the Idea of a fairly wooded area and a plateau or mesa out on the plains. I'd be more worried about other (looters) or the GOV (looters) coming to take what you have. It would be easier to see you on the plains but it would be easy to see them as well. Plenty of antelope and rabbit, fertile soil to grow for the long term. Some areas in eastern NM would be ideal for this purpose. minus the water situation.
This if I have to leave, but i'm almost sure that the GOV would force me to leave, either by evac or threat.