There are very few foot paths to beaches in NY-- since property owners can own beach to the average high tide line.-- so beaches can be, and are private-.
The land between high and low is public domain.. One political district-- i can't remember if it is an assembly or congressional (State or federal) was gerrymandered -- and for almost a mile it ran along the coast in the intertidal area-- (since there is a ruling that districts need to be contiguous) even by NY standards it was pretty outragious. It include parts of the Bronx, a bridge, and parts of north queens.