I agree with Questor, go there and check it out. Mid winter and mid summer to know the extremes.
I'm personally partial to the Tula Rosa Basin. That's Tula Rosa, Alamogordo, and La Luz. From there you can drive into the mountains and see lots of wildlife. Deer (Mule and Whitetail, as well as hybrids called Muletail.) Turkey, Bear, Elk, Mt Lion. And out on the flats south of the Sacramentos are Antalope, and Oryx (Africian Gemsbock).If you can stand the heat Las Crusis is nice as well, just more people.
Also liked the Ruidosa area, liked the horse racing. Have friends a Carazzo, don't blink you'll miss it. Just a cross roads with a few houses. If you like flat land, Artesia is nice as well. Even Roswell has something to offer.
Basically what I am saying is don't just look at one side or the other, look the whole state over. It's big and lots of different things available. The northern part is so different than the southern portion. And the East is very different than the west. And within just a few miles it completely changes.