When you say cheap hotel I am assuming a budget of less that Php1,000 (US$20) per night.
I am sure there are many cheap hotels in Davao City but the only two I know about from personal experience are the Sampaguita in downtown Davao City and the Linmarr Apartelle - just five minutes from Davao International Airport.
The Sampaguita is a no-nonsense travelers' hotel with small air-con rooms, no reservations and you have to ask for additional everything, i.e. only one towel in the room even if a double bed. Rooms from around Ph750 for a small single room. Only stay here if you are not claustrophobic.
The Linmarr Apartelle is no-nonsense air-con rooms for the night (actually Php800 per 24 hours). They offer a long-stay package (one month) for around Php6,000. Exit the airport onto the diversion road to the right and take the first significant turning right after the Iglesia ni Cristo church.
Does anyone else have more information about cheap hotels in Davao City?