Sawyer Avery, who is directing as well as playing the lead in Tuesday night’s staged reading of Neil Simon’s “Biloxi Blues” at Guild Hall’s John Drew Theater, has a gravitas about him unusual for a 21-year-old. He loves sitting in cramped coffeehouses, talking theater and art. He attends two to three plays a week in New York. After sitting down Saturday morning at Jack’s Stir Brew Coffee on West 10th Street in New York, he was on his way to go museum-hopping with his girlfriend, starting at the Museum of Modern Art.