I live in Flagstaff. If I had to choose between similar towns across the region, I'd choose Santa Fe. I'm a young guy who loves the outdoors and has no breathing problems. Allergies that I had back home are gone in the SW. I also need to work, and Santa Fe has jobs. It's also only about 50 minutes from Albuquerque, which allows you to quick pop down there for anything you can get in the smaller city of Santa Fe. It's got cheaper housing than Flagstaff, a smaller college, and more charm.
The only downside to Santa Fe is its relative isolation from the rest of the country. Head east, and there is nothing. Head west, and you've got about 10 hours of driving before California. Head north, and it's 5-6 hours before Pueblo. Head south and you've got Albuquerque and another 4 hours later you'll be in El Paso. Driving to other areas from Santa Fe just takes a long time.
Flying too, is tricky. Albuquerque isn't a major hub, so most flights require transfers. I think this is slowly changing though. It may not be as bad I think.
Some others ares to check out:
Prescott - High elevation but still on 4,000', milder weather, lots of housing, great medical services. Downsides - lots of retirees.
Show Low/Pinetop/Lakeside - Cheap property, cheap taxes, more rural living. Downside? Sleepy town with no "core" and half the population are vacationers.
Cottonwood/Clarkdale/Camp Verde/Sedona, AZ - Known as the Verde Valley, these old mining towns are slowly becoming the next Prescott, with cheaper housing, but better views. Jobs are probably more available in Prescott.
Palm Springs/Palm Desert California - desert living, but kind of a building boomtown, at the base of snow covered mountains.
Reno - cheaper, prettier Vegas. Gets snow.
Tucson - smaller Phoenix. Base of big mountains. Compact, but with traffic issues. HIghest unemployment in AZ.
Albuquerque - cheaper housing, some issues with crime in some parts of the city, close to lots of wide open spaces, milder than both Phoenix or Tucson.
If I had to stay in the southwest but could move anywhere with job a lined up, I think I'd be looking at Santa Fe. If I had to stay within my current employer's area, I'd choose Prescott. If I had to go somewhere that wasn't Phoenix or Tucson, but I didn't have a job lined up, I'd probably be looking at Reno or Palm Springs.