Close to Manila there are a couple of options for sailing. Puerto Galera seems to have the most comprehensive range of courses and renting options for dinghies. Even closer there is Taal lake where lessons and rental for small as well as larger catamaran are offered. Prices for rental vary from 12 USD for a small boat to a 100 USD per day for a 6-persons catamaran. You don't need to stay overnight as Taal lake can be easily reached from Manila in 2 hours. 

The freezone of Subic bay is home to the 42ft sloop "Shibumi" . The captain and owner is a former UK navy officer who gives sailing courses and offers various tour packages.  Prices range from 300 USD for a half day introduction to 1200 USD for a 4-day course. 

Probably one of the best places in the country to learn sailing is Puerto Galera, Mindoro. The Puerto Galera Yaucht club has 3 day courses for both experienced and beginner sailors in a Lawin sailing dinghy. The two persons dinghies are also available for rent per day.  

In Boracay street vendors are advertising sailing tours for 10 USD an hour. It is essentially a local bangka with crew that has space for four passengers on trampoline netting.