There are no accommodations at the airport, however there are two reasonably priced hotels 2 km away.
These are Ruta Jacobea ,about 60 euro/night (
http://www.rjacobea.com/), and Hotel Garcas, about 30 euro/night (
http://www.garcashotel.com/) in Lavacolla. Both are along the route of the airport bus that leaves from central Santiago and the main bus depot.
If you want to treat yourself, Ruta Jacobea has a very nice restaurant. It is also the nicer of the hotels. As accommodations go Hotel Garcas is certainly adequate as well. They are on opposite sides of the street, very close to one and other.
There is even a third option, a further 1 km from the airport in Lavacolla. It is called Pazo Xan Xordo (
http://www.pazoxanxordo.com/). It gets high ratings, looks very reasonably priced and like it would be a great place to unwind the afternoon/evening prior to flight.
Rather than having to deal with an early wake up and a walk and wait for a Santiago bus or taxi on the morning of the flight, it is much easier to spend the prior night at one of these. To reach the hotel on the evening prior to your flight you can take the regular airport bus out of central Santiago, or if returning from Finisterre, directly out of the main bus terminal. When boarding the bus ask the driver to drop you at whichever hotel you are staying. They will be happy to do so.
In the morning you have an option of walking the 20 – 30 minutes to the airport (it’s an easy straight away walk along the same road as the hotel), waiting for the airport bus to pass by the hotel and flagging down the driver, or taking a taxi the 2 km to the airport.
Buen Camino!