the closest station would be Laurelton ie (JFK is right on the bayshore closest to Laurelton - but in practice no train station is very close to JFK. Your best bet is to take the airport bus to Jamaica and get the train from there
While Laurelton (and Locust Manor) are somewhat closer to JFK, Jamaica has far more frequent train service. And next year, of course, it'll have the Airtrain.
"Let me think about it" = the coward's way of saying "no"