JFK International Airport AirTrain

Take Airtrain from any terminal on track 1 to Jamaica Station( be careful - on that track there are two alternating trains going to different routes; check the sign above the doors as the train arrives; the red colored sign is Jamaica one). Take subway E to Roosevelt Ave stop. Then take subway line 7 (direction Flushing) and get off at Mets-Willets Pt. stop.
Going back to Times Sq. is easier by taking subway line 7(direction Manhattan) and get off at the last stop(42nd street).
From Times Square take Subway line E towards Queens and get off at Jamaica Station; then take Airtrain to JFK.

See http://www.mta.info/nyct/maps/submap.htm
for reference.
JFK_E

Taxi is your first option - Taxi(from JFK to any point to Manhattan) costs flat rate of $45 + bridge toll($5.50)
There is also an express bus called New York Airport Service(NYAS) that leaves every 20 min in front of every terminal - it costs $15.
By public transportation:
Take Airtrain from any terminal on track 1 to Jamaica Station( be careful - on that track there are two alternating trains going to different routes; check the sign above the doors as the train arrives; the red colored sign is Jamaica one). Take subway E to Lexington Ave stop.
At Lexington Ave stop transfer to subway line 6 going downtown for one stop to Grand Central. Cost of the ride: $7.25 per person.
JFK_E

With one wife and one suitcase per person - the safest way is definitely LIRR:)
JFK_E

Hi,
Take Airtrain from any terminal on track 1 to Jamaica Station( be careful - on that track there are two alternating trains going to different routes; check the sign above the doors as the train arrives; the red colored sign is Jamaica one). Then take subway line E to 50th street stop. You will be two blocks away from West 48th street. ($7.25/person;~1 hour)
JFK_E

1. By train:
Take Airtrain from any terminal on track 1 to Jamaica Station( be careful - on that track there are two alternating trains going to different routes; check the sign above the doors as the train arrives; the red colored sign is Jamaica one). Then either:
-take subway line E to Penn Station or
-take LIRR to Penn Station(faster but more expensive)
At Penn Station take NJ transit train to Wilmington,DE.

2. By bus:
Take Airtrain from any terminal on track 1 to Jamaica Station. Then take subway E to 42nd street-Port Authority Bus Terminal(there is another express bus called New York Express Service that leaves in front of every terminal at JFK and goes express to PA Bus terminal)
At PA Bus Terminal take a bus to Wilmington,DE.
JFK_E

Take Airtrain from any terminal on track 1 to Jamaica Station( be careful - on that track there are two alternating trains going to different routes; check the sign above the doors as the train arrives; the red colored sign is Jamaica one).
The Airtrain station at Terminal 5(or Terminal 4, if you arriving Jet Blue international) is located on the third floor.
JFK_E

Taxi will cost you flat fare of $45+toll($5.50)for the whole taxi.
There is shuttle(look for it at Ground transportation counter or Welcome Center) that goes to any hotel in Manhattan for $18.50 per person.
Mass Transit - Airtrain to Jamaica Station then Subway E to the Roosevelt Ave stop, then transfer to F going to Manhattan. Get off on Herald Square Stop.The hotel is located on 35th str and 6th ave(next to Empire State Building).It will cost you $7.25 per person.
JFK_E

Take Airtrain from any terminal on track 1 to Jamaica Station( be careful - on that track there are two alternating trains going to different routes; check the sign above the doors as the train arrives; the red colored sign is Jamaica one).
Then take subway E to Lexington Ave. Walk 2 blocks north on Lexington Ave and make a right on 55th street; walk 1 block and make left on 3rd Ave - your address is right around the corner on 3rd Ave.
JFK_E