For those captivated by romantic visions of Sammy Davis, Jr. and Joey Bishop sipping blithely from martinis and crooning old jazz standards while tuxedoed waiters light the cigarettes of starlets, the Carlyle can be a pleasant way to drift into the past. A New York institution located on the ground floor of the Carlyle Hotel, this intimate venue was where the late Bobby Short held court at the piano in front of sold-out crowds for over 36 years. Banquettes line the walls and above are colorful music-themed murals created by the French artist Marcel Vertès, while in the dark center of the room a crush of tables give the best views of the performers. Perhaps the club originally attracted young Upper East Side swells, but today, songs like “I Get a Kick Out of You” and “Autumn in New York” appeal more to older out-of-towners. Still, when a singer belts out “I Did It My Way,” the rush is still there.