That Kind of Woman (a 1959 American drama film)  is set in New York City, staring Kay a sophisticated Italian woman who took a train from Miami to New York City.
That Kind of Woman is a 1959 American drama film directed by Sidney Lumet, who was nominated for the Golden Bear at the 9th Berlin International Film Festival. The Paramount Pictures release was filmed on location in New York City and Long Beach, New York. Kay is a sophisticated Italian woman, the mistress of a Manhattan millionaire industrialist known simply as The Man, who uses her to help him influence his contacts at The Pentagon. While en route from Miami to New York City by train, she and her friend Jane meet a considerably younger American paratrooper named Red and his sergeant George Kelly, and Kay and Red fall into a romantic relationship. 
