A travel advertisement aired on the radio in Italy states that it is "perfectly legal" to be topless in New York City; is this true?
The ad doesn't say anything else useful to the question.
Yes it is perfectly legal.
This is based on the Santorelli case, in which Ramona Santorelli was arrested for baring in public "that portion of the breast which is below the top of the areola". She was acquitted after the case went to the New York Court of Appeals (the highest court in New York) in 1992 on the grounds of equal protection. Since then there have been many similar cases decided the same way.
In February 2013, the New York City Police Department issued a command to all its officers through their daily roll call. It reminded officers that they are not to cite or arrest a woman for public lewdness, indecent exposure or any other section of the Penal Law for “simply exposing their breasts in public".
There are plenty of references for this: