The best way to get back in to NJ from NYC after 4am using public transportation would vary depending on where you were actually located in the city. One way is to take a Greyhound from City Center. Another way is to park your car at Hamilton Park and take the train.
Boston South Station has Amtrack service to NYC where you would change train for NJ destinations.
Train from Newark NJ to Stamford CT
While there is not a bus that goes from the NYC Port Authority you can take the NJ Transit from Penn Station to Trenton, NJ. Once in Trenton, NJ you can take the SEPTA bus to Sesame Place.
While there is not a bus that goes from the NYC Port Authority you can take the NJ Transit from Penn Station to Trenton, NJ. Once in Trenton, NJ you can take the SEPTA bus to Sesame Place.
If you take the PATH train, it costs $1.75. If you drive, the toll on the Hudson River bridges/tunnels is $8.00 (for a car) is enter NYC from NJ.
take it to the zoo or the park
you should take the Manhattan bridge follow the holland tunnel signs and get to NJ without paying any tolls. however on your way back you must pay the toll for entering nyc.
3.5 to 4 hours depending on traffic.
you can't
If tou are a resident of NJ, then you apply in NJ.
it would take around 7-8hours.