I assume you will be traveling on I-40, if in need of a place to stop in Albuquerque take side trip up I-25 to Bernalillo & Coronado State Park; over by Grants off I-40 is Bluewater Lake State Park and by Gallup there is Red Rock State Parkhttp://www.ci.gallup.nm.us/rrsp/00182_redrock.html
By Santa Rosa there is Santa Rosa Lake State Parkhttp://www.newmexico.org/place/loc/p...place/486.html
Coronado State Mon't next to the SP:
Bluewater Lake State Park:
El Morro National Monument if you have the time is a neat place down from Grants and to get to it you would drive by the western edge of El Malpais National Monument (lot of lava flows around Grants): http://www.nps.gov/elma/
El Morro: http://www.nps.gov/elmo/
In Arizona the Petrified Forest National Park is just of I-40 Drive through the park (28 miles): http://www.nps.gov/pefo/
Out from Flagstaff there is Sunset Crater Volcano National Monument: http://www.nps.gov/sucr/
Wupatki National Monument is on a loop drive from Sunset as well: http://www.nps.gov/wupa/
We stayed at a Nat'l Forest CG close to Sunset Crater and drove up and by the Canyon but it is a long drive if one is spending more than one day at the Canyon. We did the loop by Wupatki over to the main north/south hwy from Flag and entered the Grand Canyon from the East Entrance and came out the the West and back to I-40 a long drive, we a day trip out it.
Monument Valley Navajo Tribal Park, Utah/Arizona is a little farther over to the northeast of the Grand Canyon and Flag, but is a really neat area to see. Lot of movies were make there.
Also in AZ Canyon de Chelly National Monument: http://www.nps.gov/cach/
They have a free campground also.
In New Mexico:
Santa Fe would be interesting: http://www.santafe.org/Visiting_Santa_Fe/
State park by Santa Fe: http://www.newmexico.org/place/loc/parks/p.../place/482.html
Wal-mart will also allow over night stays.
A list of NM Nat'l Monuments: http://www.nps.gov/state/nm/
Monument Valley Navajo Tribal Park, Utah/Arizona one of my favorite places, lot of movies have been shot there.
Have a good trip and hope the Canyon is clear for you when you are there. There is a lot of neat things to see out here in the West and Southwest.