A good backpacker's inn would cost around 1,500-2,000 pesos a night. Its a good deal since it would be safe for a foreigner, has an AC and amenities. Try this one http://www.internationalinnsinc.com/
If you go the $20 rate or less, you're talking seedy motel territory.
There are cheap motels in the student areas of Manila along Espana or Morayta. Cubao or Malate. But if you're a foreigner, they'll have hookers knocking on your doors all night. Safety would be an issue too.