Mindanao is the second largest and easternmost island in the Philippines. It is also the name of one of the three island groups in the country, which consists of the island of Mindanao and smaller surrounding islands. Davao City is the largest city in Mindanao.
Domestic flights with the Philippines are easy to book via several low cost carriers. Check out Cebu Pacific, Zest Air, SEAIR-South East Asian Airlines. Philippine Airlines, etc. Be warned that excess baggage fees can be quite expensive.