I must confess, I'm ignorant as to what not to miss while on a motorcycle in New Mexico.  We're going to stop at the Grand Canyon per SO request.  After that I'm kind of in the dark as to good roads and scenic sights.  Trying to stay off the interstate and camp at night where there are coin-operated showers.  Thank you Southwesterners!

Lots of good roads in Northwest part of New Mexico.  Suggest looking at:
http://www.motorcycleroads.us/states/nm.html

Roswell, NM

And, just looking at the map, if you plan it right, you could make most of the first half of the trip almost entirely inside National Parks and National Forests.