You've heard about the reading room at the New York Public Library, haven't you? Then I need not go on. Just look at it. And you're allowed to hang around in there!
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!
Mekelburg's is equal parts hipster bodega, bar and sandwich haven. I always go for the cheese counter, the babka and the late night fried chicken sandwich, which is hands down one of the best I've had in NY.