Lots of conflicting information on JFK baggage / luggage storage on the web, but the 718-751-2947 phone number still is in operation as of Sept. 2015 and goes direct to someone that works in the baggage storage area - they confirmed for me that there is also a storage facility at Terminal 4 of JFK. I'm pretty sure this is correct because I just asked a generic question about where to store bags, he asked my airline (Delta), and then volunteered the info. about the facility at Terminal 4 of JFK.