If it were me, I would take 64 just south of Raton to the Scout ranch. From there I would take 64 west to Eagles Nest. Then west on 38 thru Red River to Questa. Then take 522 south to Taos and then 68/285 south to Santa Fe. I assume you would spend at least a day in Santa Fe. From there I would head back up 285 to Pojaque. Turn left up to Los Alamos. Take 4 towards White Rock and Bandolier. Then go west on 4 to the Valles Caldera. From there, it will depend on what you are driving. If you have something that can handle mild dirt roads, turn right on 126 by Amanda's Jemez Mountain Country Store. Take 126 all the way to Cuba. Head north on 550 till Bloomfield and then left to Farmington. If you don't have a vehicle you want to take on dirt roads, take 4 all the way to San Ysidro and head north on 550. Either way, if I had time to kill, I would take 537 north off of 550 through the Jicarilla Apache Reservation until is hits 64, then take 64 west through Bloomfield into Farmington, and hope to see some huge mule deer and elk.
Of those towns, you can find good/decent places to stay in Taos, Santa Fe, Los Alamos/White Rock and Farmington. I would not plan on staying in Cuba.