In general, gate passes are issued by the airlines, not by the airports. JetBlue's website implies that they do generally issue gate passes to allow guardians to meet unaccompanied minors:
Drop-off / Pick-up information
Please note, the parent/guardian must request a gate pass at the airport ticket counter to drop off their minor at the departure gate. If a gate pass is issued, we request that the person dropping off the child leave a cell phone number with the airport so that a JetBlue crewmember can contact them to meet their child in the event of a gate return.
Since guidelines vary among airports, please check the unaccompanied minor section under the specific airport the unaccompanied minor is traveling from to determine if a gate pass may be issued. This information can be found by entering the airport name in the search field, then selecting the Unaccompanied Minor Information link under the main airport heading.
However, there are some indications on JetBlue's website that they do not issue gate passes at JFK. From this page, in the section about minors arriving from the Dominican Republic:
Unaccompanied minors and other special service customers can be met after clearing Customs due to local airport procedures which do not allow the issuance of gate passes in JFK.
And from this page:
If you're picking up an unaccompanied minor, please go to the Baggage Services office on the Arrivals level of T5. Please ask a JetBlue crewmember if you need assistance.
It is not 100% clear, however, that a gate pass would not be issued (perhaps at the Baggage Services office) for an unaccompanied minor arriving on a domestic flight. I would suggest calling JetBlue customer service if you want to be certain whether or not meeting your niece at the gate is out of the question. You could also try calling 718-632-6355, which according to this ten-year-old Consumerist page is the direct number to the baggage office at JFK; but no guarantees that one will work.