A Corporate Pilot on a night VFR flight near JFK climbed into Class B airspace after misunderstanding the JFK Local Controller's climb clearance instructions.

Narrative

I was westbound off the south shore about to come from under the 500 FT shelf of the JFK Class Bravo. I received a transmission from JFK Tower 'Aircraft if you want to; you can start a climb; turn direct Sandy Point and I'll provide flight following to Sandy Point.' This was a relief as I had been trying to obtain a transition through the Class B earlier and was told I would have had to clear the departure path of JFK's Runway 22; the runway in use; and I was interested in obtaining more altitude to cross the Lower Bay as well and gain perspective for better navigation. I read back the 'If you want to climb' clearance and inflected a request clarification of a clearance into the Class Bravo while turning south and initiating a climb back to my desired enroute altitude of 2500 FT MSL. Other communications directed to the Tower took place directly after my implied query so while I was waiting I attempted to identify Sandy Hook; which I thought I was familiar with as a NAVAID. While coming to the realization that it was a VFR reporting point; not the Sandy Point VOR some periods of radio silence lapsed and the Controller didn't reply to me and I hadn't leveled off or clarified the clearance. As I was passing through 2300 FT MSL feet the Controller inquired as to my altitude and it was determined that he had intended for the climb to end at 1400 FT MSL. I clarified that it was indeed 1400 FT that he wanted and initiated a descent. Shortly after that transmission flight following was terminated by the Controller. Factors contributing to the event: Pilot made assumption based on Controller's issuance of a non-descript clearance and wishful thinking. Neglect to clarify clearance. Pilot workload was unnecessarily high; and performance low as a result of selection of routing proximity of obstacles (terrain; traffic; and airspace) making for narrow margins in navigation; night conditions; flight toward an unfamiliar area; and fatigue.