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There are a lot of ways to get out to JFK rather cheaply, but not exactly simple. You could always take the subway to the Air train, I don't know the cost for the Air train but it's only $2 for the subway from Penn. You may be able to get off at EWR and take the PATH and get off at 14th and cut a bit more time off of the train ride, I'd have to check the subway lines. The only problem is it's not a short subway ride, and I'm very familiar with the arduous beginning of your train ride until you get at least to Long Branch (I commuted from Metropark to NYC for years and now visit friends in Point Pleasant from NYC during the summer).... with that trip I don't know if I would want to add that subway ride, but the truth is it could be a really cheap way to get out there.

Another intereting path might be the ferry rides that go from various parts of coast, I took one home during the blackout from the east side of Wall. St and it wasn't bad, you would just need a ride to the ferry and a boat at the right time.

There are also those blue airport carpool shuttles which you call ahead for, it might be hard to pin down an exact time but JFK isn't more than 20-30 bucks.

Your best bet will be one of the city busses, I see them leave from Grand Central all the time, and those probably aren't that expensive either. You can take the 1 or 9 train (i think) from Penn Station uptown one stop to Times Square and then take the S train (shuttle) over to Grand Central for a total of $2. then you just have to walk a block down park ave and there are busses that leave from there to JFK, I would do some online research on that.

There are definitely creative ways to highly reduce the cost, one might just work out for you.

I just expense the car