The Hamptons, New York's fashionable summer beach resorts, are well known as weekend havens for city-dwellers who relish their idyllic setting on the Atlantic shore. Once quiet agricultural land, Eastern Long Island first became popular among artists, architects, writers, and society patrons in the 1920s, when it served as a breeding ground for modernism. From the avant-garde influence of luminaries like Jackson Pollock, Robert Motherwell, and Willem...