US-89N, US-160E, US-163E, US-191S, US-64E, US-491S, I-40E will get you from Flagstaff through Monument Valley to Albuequerque. You could also stay on US-64E to US-550E/S to I-25S to Albuquerque. I don't consider any of them to have any stretches of real mountain driving. It has been a while since we have travelled some sections of this route, but the US highways have always been in reasonable condition when we have. You can use the state department of transportation websites to check for construction projects.
Arizona DOT,
New Mexico DOT,
New Mexico Road Advisories,
Albuquerque Road Construction.