I stayed at the Holiday Inn just outside of Canyon de Chelly and it is nice enough, good rates and is right outside the park.
In Santa Fe area, I would take either the High Road drive up to Taos, Espanola to Chimayo to Taos or go to Abiqui from Espanola, both really nice drives.
Been to many years since I was in White Sands, but I do know that Almagardo such have good places to stay and is not to far away. Don't recall anything really right at the park other than camping. Plan on getting back there this spring, but that does not help you now.
Have a great trip and enjoy..good light.