I had heard there is a "party bus" that goes from NYC to Avalon, NJ on Fridays and returns Sunday evening but I don't have any details, sorry
Yes, it is safe to ride public transportation in New York City. New York City is the safest major city in the U.S., and has been for several years now.
the subway
The New York City Metropolitan Transit Authority offers Subway and Bus transportation in and around New York City to the Public. They also offer Access-A-Ride services for the handicapped or disabled.
One would guess that they had horse-drawn hacks like they did in England.
transportation from new york to vernon new jersey
The train
It's up to you but New York city can be difficult to drive in and they have a wonderful public transportation system. I found it easy to walk, take a cab or ride the subway to get to anywhere I needed when visiting.
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.
Public transportation in New York City is regulated and administered by the NYCTA (New York City Transit Authority), which is a sub-division of the MTA (Metro Transit Authority). The MTA is the New York State transit authority. See the Related Links below for more information about the NYCTA and the MTA.
Philadelphia is considered the transportation center for the northeast
New York City trains represent the New York City Subway that spans across the distance of the city. It represents a universal transportation method of New York.
In addition to New York City, there is the MTA - Transportation Network.