If there is any way you can get rerouted thru EWR ( Newark)? It is a nicer airport and ALOT closer to downtown...
JFK is a hard airport to negotiate from no matter what...UNLESS you can have someone pick you up and/or drop you off...
It is actually easier than it used to be to train>subway>JFK:
Most Reliable Method – LIRR and the Airtrain Combo to JFK Airport
This method is not just the most reliable, but also a relatively cheap and quick way to travel from Penn Station to JFK International Airport during the day or night. Catch the LIRR train from Penn Station to LIRR's Jamaica hub, which takes 20 minutes. From there take the JFK Airport Airtrain on the upper level that gets you to the airport terminals in 12-15 minutes. LIRR trains and the JFK Airport Airtrain run 24 hours a day. Be sure your LIRR train stops in Jamaica though, because some trains bypass that station.
The cost of using the LIRR/Airtrain combo to get to JFK International Airport depends on when you travel. The JFK Airport Airtrain always costs $5, payable with a pay-per-ride Metrocard (Unlimited-use Metrocard's won't work on Airtrain). The LIRR fare varies with travel time: during the afternoon rush, the LIRR fare to Jamaica is $7, making your total cost $12. During other weekday hours, the LIRR fare is $5, for a total fare of $10. On weekends, you can ride the LIRR to Jamaica for a special City Ticket fare of just $3 – making the total cost of your trip to JFK Airport only $8.
LIRR trains run to Jamaica every 15 minutes during the day, and every half hour at night, except between 2 and 5 AM, when the trains run hourly. Travel time is uniformly 35-45 minutes, and transfers between the LIRR and the JFK Airport Airtrain are easy to make. If you consult
www.mta.info for nighttime LIRR schedules, your trip should be painless, no matter when you travel. Announcements at Penn Station, on the LIRR trains, and the JFK Airport Airtrain are always clear and concise.
Cheapest Method – Subway and the Airtrain Combo to JFK Airport via Sutphin Blvd.
A Cheaper solution for catching the train from Penn Station to JFK is the subway/JFK Airport Airtrain method. From Penn Station in NYC, the E train will take you to the LIRR/JFK Airport Airtrain (Sutphin Blvd.) station in about 45 minutes, and then it's a 12-15 minute ride to the airline terminals. The cost is always $7, and the E train runs 24 hours a day. E trains run every 8-10 minutes during the day, and every 20 minutes after midnight.
For full/more info:
http://www.nysubway.com/airport/jfk.html