Its quite a trip out there but so very worth it if you wanna have the very special beach-experience! You can go there by car and then take the ferry either to Pines or Cherry Grove (I would prefer Pines!) or you do all by public transportation - there a "getaway tickes" for 36Dollars and the transfer works really smooth - may even be faster than by car!
City Island is a seaside town in the Bronx. Known for its fishing, seafood, and main street it is a self-contained working-class haven. The buildings range from late 1800's houses to 1960's storefronts, and you can smell the ocean everywhere on the island. Restaurants and local pubs dot City Island Ave, and even the few empty storefronts stay vibrant.