I too lived in New Mexico for a while. I love the land. Love the underpopulation. Not so sure about some of the people there, or their ideas.
My wife and I lived in Las Cruces. I don't recommend it for retirement. We got married in Cloudcroft, a mountain community in the Sacramento Mtn. Range. A lovely place with a "winter" of light snow and low temps, but its nice in summer and the landscape is beautiful. You can drive east to the Permian Basin and take in the enormous oil/gas presence and Chihuahuan desert. A little south is Carlsbad and the famous caverns. If you're a caver (such as I am) it is a very good place to be. A little north and you're in Roswell. I've looked for aliens but found none of the extraterrestrial type. If you're a storm chaser, this is an area that gets beautiful thunderstorms and sort of frequent tornados. Drive to the west and you'll end up in Alamagordo where they have big "sky parties" where amateur astronomers from all over the world come and share telescope time. Just west of Alamagordo is White Sands National Park. It really is a special place. The best photography there is very early morning and late evening. If you live only 30-40 minutes away, its easy to loiter there and get your shots. To the north is the Apache community of Riudoso, where you can immerse yourself in "the culture of the horse". And gamble too I think. Not my thing though. A great mix of Mexican and American cultures if you want to experience that. Or you can surround yourself in true "old western" rancher/cowboy culture if you wish. Or you can experience Native American culture. There's a fun counter-culture spread out through New Mexico that seems to integrate rather well. You'll find the UFO types in Roswell (they have a museum there).
Crime is definitely in NM. I used to live in southern California though, and experienced more crime there than anywhere else in the U.S. I never felt terribly unsafe in NM, but I have lived in the rural western N. America most all of my life and know what to avoid/do.
Silver City is a well-known retirement destination. That's in the southwest part of the state. It can get hot there, but if you're a birdwatcher you will be in heaven. Among the most diverse avifauna in the U.S. (including Hawaii and the Aleutians). I find it too close to some ultra-conservative, neo-nazi communities for my taste though. I can visit, but I don't think I'd live there.
The best medical care is found at the population centers: ABQ, Santa Fe, Las Cruces. Alamagordo has medical infrastructure because of its proximity to so many military sites (Holloman AFB, Fort Bliss, White Sands Missile Range). One reason why Cloudcroft seems feasible.
Oh, and you can see some spectacular missile tests at WSMTR. I once watched a missile interception test that was kind of neat (not that I'm into war machinery, but you just have to awe at what you see). They close Hwy 70 that goes through the range whenever there's a test. I worked in eastern NM when I lived in Las Cruces so went through there almost daily for a while.
Oh, and I forgot to mention the highest elevation golf course in the world is in Cloudcroft....in case that interests you.
And you definitely need to get a gun. Just so you fit in if nothing else. You don't actually have to use it if you don't want, but make sure folks see it over your fireplace (or whatever). Part of the culture, kind of like Montana.
