I've been to Santa Fe more times than I'd care to admit this year. Everyone else is right - fly into ABQ and rent a car. There's a return from ABQ to ATL that leaves 1-ish in the afternoon that avoids you having to wake up well before the crack of dawn.

If you're hellbent or stuck flying right into Santa Fe, perhaps NYC-LAX and then transition to AA for LAX to sAf. They do one flight a day, leaves LAX around noon and leaves SAF around 3 or 4. Pretty sure but not positive that you'd have to carry on or leave enough time to claim your bags and reclear security in LA though.