I live in New York. I drive in New York. I drive to Newark and LGA, but from Manhattan to JFK, I always take the LI Railroad to Jamaica and then the airtrain. I just wouldn't bother with the hassle of renting and returning a car no matter how cheap to travel from LGA to JFK. I would suggest you take a cab either to Jamaica Station to connect with the AIrTrain or all the way to JFK. It's less than 8 miles to Jamaica Station and could take anywhere from 15 minutes to an hour +. Then the AirTrain will be another 10-15 minutes. If traffic is light, take the cab all the way to JFK. If traffic is heavy, take the cab to Jamaica Station and then the airtrain.