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"Big Apple" is a nickname for New York City. It was first popularized in the 1920s by John J. Fitz Gerald, a sports writer for the New York Morning Telegraph. Its popularity since the 1970s is due in part to a promotional campaign by the New York tourist authorities.
What's the origin of the phrase 'The Big Apple'? ... He reports hearing the phrase used by stable lads while on a visit to New Orleans in 1920, although there's nothing in that report to link the phrase to New York.