The last time I flew into JFK, I took the "free" AirTrain from the terminal out to the subway. I was rather surprised and annoyed, on getting to the subway transfer, to discover that it wasn't free after all. Between terminals is free, but to transfer to the subway you had to pay a special exit fee of $5. Only after that could you then buy your subway ticket, and head into town. By the time I was at the subway station, it was too late to change plans, so I had to grudgingly pay. They kept this very quiet until you got to the end, and it was too late to change your plans!
For my next trip, I should have more time (I land mid-afternoon, but I'm not meeting friends until after work). I know that with other airports with high charges for the public transport connection, there's often a hidden way to avoid it that locals know. (In Sydney for example, there's a bus that'll take you a couple of miles to a normal railway station, or you can walk just over a mile to another one).
What I'm wondering is if there's something like that for JFK? I'm aiming to get to either lower Manhattan, or Brooklyn Heights. Can I get either to a subway station, or all the way down to somewhere like that, without having to pay the airtrain exit fee? (The subway from out by the airport to Brooklyn/Manhattan is only $2.25, and the current airtrain exit fee is an extra $5, so anything involving private buses/shuttles will likely work out much more!)