Well, according to a New York Magazine Intelligencer item, it might be Madison Avenue cafe Via Quadronno. The establishment "closes for just four days each year: Thanksgiving, Christmas, New Year’s, and a certain spring day."

A spokesman claims coincidence. “We close that day every year for internal construction,” he says. “The last day of the first week of June.” The Puerto Rican Day Parade is on the second Sunday of June each year.