If you are visiting NY during the summertime, then Coney Island in Brooklyn is practically obligatory for at a daytrip.
There you have the colorful 3-mile beach, the lively boardwalk and the famous Luna Park with the breathtaking thrill rides. There is something reminding me of the 80s era in Coney Island, when all famous and rich people wanted a reserved beach spot.
There are various festivals and parades taking place there, including the Mermaid Parade in June.
Getting there: Hop on the D, F, N or Q trains to Stillwell Ave. station. A variety of buses also travel to Coney Island from Manhattan and the other boroughs.