I can get back to you with the exact rules later this week (midterms and all), but off the top of my head:
101.33 - No person may operate an unmanned free balloon
(a) Unless otherwise authorized by ATC, in a control zone below 2,000 feet above the surface, or in an airport traffic area;
Airport traffic area here would include the New York Class B airspace and Long Island Class C airspace. You can check this on a VFR map. Now, this does cover only up to 10,000 ft, but it means your balloon has to reach at least 10,000ft by the time it gets there and still be at above 10,000ft by the time it leaves. If the balloon lingers in Class B, the FAA is not going to be happy. You could devise an aborting mechanism as suggested above, but then you run into
101.33(e) In such a manner that impact of the balloon, or part thereof including its payload, with the surface creates a hazard to persons or property not associated with the operation.
so if you abort over a city, and the parachute doesn't deploy or it lands in the middle of the street, etc., that's also going to be an issue.
So if you managed to get the perfect flight path where you can respect Class B airspace and you're confident enough in your flight predictions, you could technically go for it. However, I've been running flight path sims for a while now and I don't see how you're going to get it away from the Atlantic.
I'll update with addtl. info, we have a Google Doc about FAA regs and NYC airspace specifically somewhere.
EDIT: This might also be worth actually calling the FAA or JFK, LaGuardia, or Newark ATCs about.