False. Coney Island and other scattered beaches. That said, at least Coney Island is a scummy, nasty beach. Expect broken glass and syringes buried in the sand.
It's legal to go topless (women) at your public beaches.
False. However there are specific public beaches set aside for nudity, have been for past 30 odd years. They sunbake topless at metropolitan beaches but no action is ever taken unless somebody makes a complaint.