There are a bunch of different combos depending on what exactly you want to do and if there are other places you want to visit.
For example, if you want to do Palau as well, it is actually cheaper to book a flight to Palau since that flight would take you through the Philippines. You can do a stopover before or after and get cheap ferries and local diving deals to other parts booking from Cebu or Manila. However if you decide to do Palau after you get to the Philippines, then the cost of that flight will be as much as NY-Manila!
Another way is to look for cheap airfare going to nearby countries like Hong Kong, Singapore or even Japan or Korea and then book a Philippine dive tour from that country. Lots of these places have inexpensive dive tours that go to the Philippines. For example, a 6/7 day tour of 5 dive days up to 5 dives per day falls between HK$3000-$5000 depending on the class of diveboat you book. r/t airfare is included in this price, but you will have to bring extra for the ferry crossing once you get to the Philippines, the DM tip and cost of food for your last day there.
So if r/t NYC to HKG in Economy is approx US$900 during a fare sale and the cost of an upper-end trip is US$642 (exchange rate US$ to HK$ 7.78) you're looking at US$1600 for the entire trip plus the additional expenses for your day in HK and the DM tips and stuff in Manila.
If you go thru Singapore, they have lots of inexpensive dive deals to nearby Malaysia and Indonesia
If you go with a dive tour, you'll be safe as long as you don't wear sparkly jewellery or wave lots of cash around. However, if you're looking to go "local" and solo backpack your way through the Phils I would not recommend it.