From NYPD's License Site:
Can I go target shooting outside NYC?
A NYC carry business license is valid throughout NYS. Premise residence and premise business licenses are only valid in NYC except as indicated in the next section.
I'm reading this to mean that your permit is no good outside of NYC but if it's legal for you to have the handgun where you're going it shouldn't be an issue. I would think you'd have more trouble in New Jersey then you would from NYPD for transporting it outside of NYC. Basically it seems to me that the licensing bureau is saying that if you leave NYC and go elsewhere in NYS then your handgun would be illegal.