The legendary Hamptons, a cluster of wealthy enclaves on Long Island’s South Fork, remains a celebrity summer playground, with splashy restaurants and nightclubs galore. But lovely beaches, fishing and kayaking attract off-the-A-list visitors, as well. Old money oozes throughout Southampton, while new wealth reigns in East Hampton. Montauk is a hit with fishermen and surfers. The Long Island Railroad travels the Hamptons in an hour. The Sag Harbor Whaling Museum and Montauk lighthouse are popular stops.