NYCB was founded by Lincoln Kirstein and the 20th-century’s greatest ballet choreographer, George Balanchine. And it is for Balanchine’s work that you still attend performances at the New York City Ballet; his choreography is the staple here and remains as diamond-sharp, elegant, and moving as when it was first performed as many as 50 years ago. Balanchine’s version of The Nutcracker is a holiday classic and one of the most difficult tickets to get each Christmas season.