Robert Pattinson is making the rounds of the city’s swankiest restaurants. Monday, the “Twilight” star dined at Vanity Fair editor Graydon Carter’s newly opened Beatrice Inn. The next night, Pattinson, sporting an MTV varsity jacket, dined at Carter’s Waverly Inn, where he created a stir among fans by being photographed outside with a newly shorn ’do — in stark contrast to the expertly tousled mane he made famous in his vampire franchise. Then, on Thursday, he hit Cipriani Downtown.