JFK International Airport AirTrain

Hi Rudy,
You can store your bags at the baggage storage at T4 - it is 24hrs open.
Here are the ways to get to Whitehall Terminal:
1. 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). Then take subway line Z to Broad street stop(cost-$7.25).Walk down couple of blocks until you reach South street;make right and you will see Whitehall terminal.
2. By Taxi:
Yellow cab (from JFK to any point to Manhattan) costs flat rate of $45 + bridge toll($5.50). The price is for the whole taxi, not per passenger.
3. Shuttle:
There is shuttle(look for it at Ground transportation counter or Welcome Center) that goes to any point in Manhattan for $18.50-$25 per person.

On your way back from Times Square you can take Subway line E(direction Jamaica,Queens) and get off at Sutphin Blvd; take Airtrain to JFK Terminals.
JFK_E

1. 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). Then take subway line E to West 23rd street stop(cost-$7.25).
2. By Taxi:
Yellow cab (from JFK to any point to Manhattan) costs flat rate of $45 + bridge toll($5.50). The price is for the whole taxi, not per passenger.
3. Shuttle:
There is shuttle(look for it at Ground transportation counter or Welcome Center) that goes to any point in Manhattan for $18.50-$25 per person.
JFK_E

Taxi is one of the options - it will be on the meter(expect to pay between $25-$35).
Second option is 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). Then take subway line E to Forest Hills stop;transfer to subway line G,R or V going same direction to 63rd Drive stop.Cost - $7.25/passenger.
JFK_E

Subway is running non stop.
At that time you have two options:
1. By public transportation:
Take Airtrain from any terminal on track 1 to Howard Beach 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 green colored sign is Howard Beach one). Then take subway line A to Columbus Circle stop, then transfer to line 1 going the same direction; get off 96th street stop (cost-$7.25).Walk one block south on Broadway and turn right on W95th street - the hostel is block and half away (on your left).

2. By Taxi:
Yellow cab (from JFK to any point to Manhattan) costs flat rate of $45 + bridge toll($5.50). The price is for the whole taxi, not per passenger.
JFK_E