Shiprock lies in a fairly desolate area (desert, duh !) and the town of the same name is umm... unremarkable.

Use Farmington NM as your base and you can also do Aztec and Chaco Canyon but quite likely to still be blisteringly hot in early Oct. Bring LOTS of water.

If you have time take US84 from Farmington to Santa Fe, it's spectacular. The other option (US550) is incredibly boring, but you would be able to say you'd been to Cuba .