It isn’t quite the holidays without “The Nutcracker” or “A Christmas Carol.” The American Dance Theatre of Long Island presents the former with its ballet students and professional dancers from New York at Guild Hall on December 14 and 15. The Gilbert & Sullivan Light Opera Company of Long Island performs an adaptation of Charles Dickens’ masterpiece at Old Whalers Church on December 22. 44 Union Street, Sag Harbor; 631.725.0894; oldwhalerschurch.org