Which bike are you planning to ride? I got my degree at NMSU in Las Cruces then moved to Santa Fe and worked for the state of New Mexico. In 1979 my wife and I moved back home to be with family.
Northern NM you can visit Los Alamos where the A-bomb was created. Indian cave dwellings are near also. Not sure when the Fiestas de Santa Fe is, but the state fair in Albuquerque is in September. Southeastern NM is White Sands Monument. Further east is Carlsbadd Caverns. Great camping country. Enjoy your trip.