In the 1920's, John FitzGerald wrote for the New York Morning Telegraph newspaper.
His regular column was called 'Around the Big Apple,'
and covered the horse races in New York State.
By the 1930's, The Big Apple was the name of a fashionable Manhattan night club, and the jazz scene presumably popularized the nickname.
Decades earlier (in 1905), esteemed horticulturist Spencer Ambrose Beach wrote The Apples of New York. The two volume set is lavishly illustrated with richly colored plates of familiar varieties, and the occasional exotic entry.