As a burqueno, I will say this - if you can avoid ABQ, do. That means if you decide to move there, live in either Corrales, the east mountains, or certain areas of Rio Rancho.
Stay away from the Kirtland AFB area. The war zone (which gets bigger every year) exists between the North side of the base and the South side of Zuni, between approximately Wyoming and Louisiana BLVD. Avoid the area by Tramway and Central called Western Skies. Also avoid the area between I25 east to San Mateo all the way between I40 and Alameda.
Avoid any neighborhood connected to Central Ave, regardless of east or west side.
If you must live in Albuquerque and not one of the surrounding cities, look for homes east of Tramway and between Montgomery and Lomas. Also, some areas on the west side around Montano can be nice as well. But that is relatively nice (as in, you won't see that many robberies or hear that many gunshots).
For schools, last I heard all the elementary schools and middle schools had lost their accredidation, so while some schools are better than others, they're all ****. Definitely avoid West Mesa and Highland school districts, and give a hard look toward avoiding Del Norte and Sandia as well.
When looking at suburbs, avoid Belen and Los Lunas unless you're getting enough acreage to defend your home from a distance. Look east toward Edgewood or Tijeras, but not so far as Moriatry. Rio Rancho has some nice areas, but a ton of ghetto as well, and I'm not too familiar with which is what anymore.