I had my first three chances to ride (road bike) in New Mexico this past year, so I'm far from an expert and take it with a grain of salt.

Northern NM has some pretty epic climbing. Los Alamos itself is a good slog from both the east and the south access highways. Taos has some flatter but windy rides to the west and great climbs to the east and north. The two rides I did in Albuquerque were pretty flat but not too scenic--there's a lot of city there.

In every case, I found the roads and trails to be fair, not exceptional, and some of the mountain highways sported some fast traffic with little or no shoulder. The drivers seemed polite and savvy though. Most of the rides were early morning to avoid the heat of the coming day, and I seldom saw another cyclist. Maybe they are tougher than me and ride at high noon.

On a bright note, I rode some of Colorado's Triple Bypass (120 miles, 11k ft. climbing) with a NM based group I met on the first climb. They were all super friendly and fun.