The Public Theater has postponed the first preview of “A Midsummer Night’s Dream” due to the helmer Daniel Sullivan’s accidental fall Tuesday. Show will now begin perfs Aug. 8, one day later than scheduled.Sullivan fell down a trap door on the set of “Midsummer,” which had just begun tech rehearsals for its summer run at the Delacorte Theater in Central Park. The director suffered fractured ribs and a collapsed lung, but is said to be recovering well. The Public anticipates he will leave the hospital and return to rehearsal in a few days. “Midsummer” stars Martha Plimpton, Tim Blake Nelson, Laila Robins and Jay O. Sanders. Opening is skedded for Aug. 23.