Re: jfk airport
Cheapest way is probably the airtrain to Penn Station then subway. That will cost $14 on the airtrain and a dollar on the subway.
Much better to get a shared shuttle , there are plenty of them operating from JFK and will drop you at your hotel. After you come through Customs you will see a Ground Transportation desk - go there and they will advise which one to take , make the call for you and sell you a ticket. Theres a waiting area (you will only be waiting a few minutes) , the driver will come in and call your number. It costs $17/$18 one way , and you can book your return as well if you wish.