Hi Ohio welcome to the site.
Whereabouts in NY City? Its pretty big.
There are guys who fish the battery right in downtown Manhattan and the east river and a bunch who fish staten Island, Brooklyn, Queens, Bronx and Long Island. Brooklyn, Queens and Long Island have head boats. Sheepshead Bay in Brooklyn and Jamaica Bay in Queens. (cost per head) about 70 bucks . Long Island has several fleets as well. Also several captains run charters out of the Hudson but New York City is at the mouth of the river and its a ways up river to the Hudson fleets.
Private charters are always better. IMO. Its a good idea to get 4 to 6 guys and pay for a charter. Less nuisence and nonsense. ;)
Read about what the guys have to say there and you'll be ready in no time. There are many urban shoreline paths and piers along the city. Hopefully your close to some of them and you get the chance to fish right there as well.