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Leave the overhyped, overcrowded Campbell Apartment to the Metro-North crowd; the low-lit Carnegie Club is classy and quiet. A bartender in pinstripes expertly mixes classic cocktails, such as the My Way manhattan (Jack Daniels on the rocks with “no vermouth, no bitters and no cherries”). On Saturdays, a singer backed by an 11-piece orchestra does Sinatra covers. Hidden among the well-stocked bookshelves are plenty of private corners for curling up with a mojito and a friend.