Route 66 Motel
The Historic Route 66 Motel is the place to stay in Tucumcari, NM.
It's between Oklahoma City and Albuquerque and it's cheap - our room for three adults and a dog was $46. The beds are new and so comfortable you'll want to try to steal them when you check out. They have free internet and continental breakfast and the whole joint has been preserved in its original 1967 style.
And the owners are nice! Go here if you're tooling down I-40.