Drive; the area is too big and hilly for there to be viable alternatives. This part of the state has severe problems with DUI, so keep your eye out for erratic motorists. Another, possibly related problem is the astounding fraction of vehicles that are seriously decrepit. You probably won't have to log many hours of driving in northern New Mexico before you see something unexpected and hazardous fall off a car or particularly truck, maybe in your path. Defensive driving is a good idea, even though the traffic density is low except in and near Santa Fe.
Relying on others for your transportation doesn't work well here. Hitchhiking in this area is an iffy proposition. Traffic density in the rural areas is low, so you may have to wait a long time for a ride, and the DUI issue makes it downright dangerous to be at the roadside at night.
The North Central Regional Transit District (http://www.ncrtd.org/) "Blue Buses" provides free bus service Monday through Friday with routes that connect the counties and communities of Santa Fe, Taos, Los Alamos and Rio Arriba.
