Another vote for Raja Ampat at that time of the year in Indonesia. There is a choice of liveaboard boats and not all can be found on the same website. Dive The World usually offers a good choice and worth exploring for your dates.
From New York it would probably better to plan a flight route via Europe. A good choice would be to fly KLM via Amsterdam to Denpasar, Bali. That way, you can book your baggage from NY to Bali, transiting in Schiphol Airport, Amsterdam (where there are airside hotel facilities if you have a few hours between flights and want to snatch some sleep) and then flying direct to Denpasar, bypassing busy Jakarta. From Denpasar it is not difficult to find local flights to Sorong, the final stop for Raja Ampat.