Tha absolute cheapest is by Airtrain/subway ($7.25); take Airtrain from your terminal to Jamaica Station and transfer to the E subway which, when it enters Manhattan, has stops along 50th St. and then heads downtown along 8th Ave. You can also take LIRR ($13)from Jamaica to Penn Station located at 33rd St. between 7th & 8th Aves. The NYAS bus ($15) stops at all terminal and goes to Grand Central Station, Times Square, Port Authority Bus Terminal and Penn Station. Taxi is $50+ and all taxis at JFK are NYC taxis.
Tha absolute cheapest is by