I doubt you'll find many/any G-reg helicopters for hire in the US, let alone Jersey - though if you were willing to do the paperwork/TSA check with sufficient notice - you may wish to chat with the following northern NJ schools as possible rental options?
Nassau Helicopters
Princeton, NJ
Helicopter Flight Services
Lumberton, NJ
Copter Pros
Lumberton, NJ
Pegasus Helicopters
Linden, NJ
Alternatively, you may wish to consider some flying with one of the school CFI's onboard (as a safety pilot). No rental checkout would be necessary in that case and only $25-40 extra an hour - not a bad option for simplicity sake.
You'll enjoy the area with nice views of NYC if you go a little east.
Regards,
NYC flyer