The Coney Island beach in Brooklyn, NY, is peaceful at night and packed by day. At night, one can stroll down the boardwalk or walk in the sand uninhibited and watch the waves gently lap the beach. Benches line the boardwalk; during the day, refreshment stations are also abundant. Restrooms are available if needed, as well.
In addition to the beach, one can also visit the amazing carnival right near the beach. Rides of all types for all ages make this an added bonus for everyone (who likes carnivals) in the family. Finally, there is a great aquarium also nearby that has both inside and outside areas.
The beach is free; the carnival rides and aquarium are not, of course.