Using a different terminal (post security area) at JFK

Access to the sterile area is open to anyone who undergoes TSA security screening, and in theory, the TSA should allow anyone with a valid ticket showing a same-day departure from the airport access to any security checkpoint. This has been the standard for several years now.

Anecdotal reports are mixed, however; this is a frequent topic of conversation at FlyerTalk, usually in reference to lounge access. The TSA officer checking your BP has some discretion as to whether to allow you through to screening, and it seems not everyone will permit someone with a ticket for a flight not departing from that terminal access to screening for that terminal. A larger difficulty is "pre-screening" done by airport or airline employees, who may discourage you from going through, or who will assume that you are lost.

I still haven't been able to find anything official from the TSA on this matter, but it is true that the published requirement is only a boarding pass (or gate pass) for a same-day ticket, without any mention of whether you should or should not have access to areas other than your departing gate area. LAX, for its part, has explicitly said that it is allowed on its Twitter feed:

Dine/shop @ any terminal regardless of the terminal you're flying from, as long as you have boarding pass for same day departure— LAX Airport (@flyLAXairport) November 2, 2014

And at Pittsburgh, it was recently announced that non-ticketed persons would be allowed airside access again, though this apparently required painstaking negotation, and is not likely to be repeated soon at busier airports.