Having just written about the poor service of Super Shuttle, I realized I should also be commending the merits of the Air Train. Because it is mass transit, it defies any traffic jam that could prevent your airport shuttle or taxi from getting you to the airport on time. From Penn Station on the LIRR, you can get to JFK in 40 minutes - now that's amazing for a one way trip for under $15.
If you opt for the subway from Midtown, that should run you about $10 and that usually takes a little longer - about one hour and 15 minutes. If you're not familiar with NYC, stick close to other passengers who also have luggage with them. This is a very popular method for New Yorkers and visitors to get to the airport, so you should be in good company.
For late or early morning hours, the LIRR remains a pretty safe option for getting to Manhattan; for obvious reasons, avoid the subway between 11 pm - 7 am if you are not familiar with the city.
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