American Airlines and Continental have direct flight from JFK to Puerto Plata. The flight is about 3 hours and 20 Minutes. From Newark you can take direct flights on Continental and American. Alternatively, you may take flights that go through Miami or San Juan, Puerto Rico. In general, flights from other cities such as Chicago, Philadelphia or LA will be either through New York, Miami or San Juan. These will probably be on either American or Continental. Ticket prices will typically range anywhere from about $450 to $850 round trip.

Jet Blue also has direct Flights from New York, JFK to Santiago in the DR. The flights are incredibly cheap at about $150 each way. The bad news is that you will arrive at the wee hours of the morning and the taxi ride from Santiago will take well over two hours so you need to decide if the savings are worth it.

Some travel planning tools include:

Expedia
Orbitz
Travelocity
Priceline