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Ostensibly Houston’s oldest continually operating bar, this landmark (which began life as something called La Bamba in 1949) recently underwent a handsome renovation that updated its darkly chic interior while expanding its patio and cocktail selections. Always the place for a mojito or screwdriver, these days Leon’s is a calming antidote to the maddening Midtown party scene as well, and a terrific spot for a classic cocktail.