Did you forget about the forgotten borough? Staten Island has lovely beaches that are just a short bike ride from the ferry terminal in St. George. You avoid the trafficky streets to beaches in Brooklyn and Queens and the outrageous fare ($52 RT with bike!) to Sandy Hook. Meet at the Whitehall Terminal bike corral for the free 11:00 SI ferry. Bring swimwear (there are changing rooms), towel (or just use a bike jersey), beach blanket (optional), lunch money (or bring your own), and bike lock.

St. George to South Beach: http://roboviva.ninja/roboviva/pdfs/30553399.pdf
RWGPS: https://ridewithgps.com/routes/30553399