Just flew out of JFK T6 last week. There are a couple of breakfast places - one booth-style place offering pre-wrapped pastries, bagels, etc. and a cafeteria that seemed to offer hot meals. The first was open when I arrived at 6am, but the second didn't open until around 6:30am.
I bought one of the pastries to bring on my flight, and it was quite tasty. It's worth noting that JetBlue does offer free snacks on its flights - on my flight to SJU we had a choice of potato chips, bagel chips, biscotti, or a cookie.
-Zombie-