There are no hotels or private guesthouses in the airport area. The nearest accommodation is in the nearby town of Dalaman, but can only be reached by taxi (10 minutes drive / 20 eur on the way from the airport, but from 120 try on the way to the airport). No hotel in Dalaman offers a free airport shuttle.
The nearest towns that can also be reached by bus are Fethiye and Marmaris respectively, where buses run according to the timetable, i.e. they cover all flights.