You have several options when planning your travel to Santa Fe.   

If you fly in to Albuquerque Sunport (ABQ), you can rent a car or pick up a shuttle there for the ~1 hour ride north to Santa Fe . Road Runner Shuttles pick up and drop off at most Santa Fe hotels, Sandia Shuttle Express  picks up and drops off at a bus stop within walking distance to Plaza area hotels. 

Alternatively, you can fly to Santa Fe Airport (SAF) from DFW or LAX (on American) or DEN (on United) then rent a car (Hertz or Avis only), take a shuttle, or taxi to your hotel.