Santa Fe options:
1 - You can drive to the Santa Fe Ski Area, parking lot is 10,200', and base out of there or just bike off and leave your vehicle there. The lower part of the ski area parking lot is used for those hiking/backpacking onto the Windsor Trail.
2 - Or if you have a family with you, car camp in Hyde State Park, passed along the way to the Santa Fe Ski Area, at an elevation of ~8500', and bike from there.
3 - Family car or bike camp out of Big Tesuque campground, between the two above, at ~9500'.
Lots of awesome high elevation riding potential out of Santa Fe, you just need to stay out of the wilderness area. Biking up Aspen Vista will top you out at 12,000'! Cross your fingers everything doesn't get closed this summer, due to fire danger. Looks to be a bad year again, unless the gods start up the snow machine.
Sandias/Albuquerque options:
There's quite a bit of riding in the Sandias, at 7000'-10,000', outside the wilderness area. However, the Sandia trailheads are not a good place to leave a vehicle overnight [OK during the day, but too close to bored metropolitan youth to leave overnight] and you have to stay out of the Wilderness area, but I've biked from our house in Albuquerque, at ~5500', to bike camp in the Sandias, between the Tram and Crest, at ~10,300', as pre-CTR altitude acclimatization. Riding from Albuquerque is asphalt, then you have singletrack or asphalt options at ~7000'. I know of other places/friends to park your vehicle at, closer to 7000', if you're interested.
Taos options? Later...
double Boundary is what I meant to say. Ideally I would prefer to not ride back into town and camp out in the mountains.