It’s a Friday night in Everett and Nerlens Noel is ready to hit the town. George Wright-Easy, a 28-year-old friend who has known the 6-foot-10 shot-blocking phenom since he was a gangly grade schooler, picks up Noel at his house. Widely considered the top prep prospect in the country, Noel has the world in the palm of his enormous hand. So where does he go on one of the last nights before his world changes, before he leaves for the University of Kentucky next month and presumably the NBA draft 10 months later? To the movie theater to see the latest installment of the “Spiderman” series with kids Wright-Easy mentors through New England Community Services — a Dorchester-based nonprofit that has a contract with the Massachusetts Department of Children and Families.