We are interested in going to a new island (or caribbean side of Mexico) for vacation. But, we really want to go somewhere that has a direct flight from one of the NYC area airports (LGA, Kennedy or Newark). Please give me ideas of where we can fly to direct - we have been to Jamaica and Puerto Rico, and T&C already and would like to try an island we have not been to yet. Help!!!

I fly JFK direct to SXM (St. Maarten) every year.

Also, St. Thomas, Dominican Republic, Aruba, Antigua, Barbados, Trinidad (probably others as well).

I can tell you about flying from Newark/Continental non-stop:
Grand Cayman
Punta Cana, Dominican Republican [recently added non-stop]
Barbados
St. Thomas [+ short ferry ride to St. John]
Jamaica
St. Maarteen
Aruba
Cancun [ok not an island, but Riviera Maya on the Caribbean side, an hour or so South of Cancun, has gorgeous beaches].

Caribtraveler has some great info which I think is what you are looking for (nonstop). However, the term "direct" I would like to clarify does not mean nonstop. Direct means you don't have to change planes but it stops and it could stop more than once...do check. To my knowledge there are no nonstop flights from LGA to the Caribbean but can be some direct flights. Have a great trip.