George Balanchine’s production of The Nutcracker, choreographed in 1954 for the six-year-old New York City Ballet, is lovingly rooted in the original Mariinsky production, created in 1892 by Marius Petipa, Lev Ivanov, and Pyotr Ilyich Tchaikovsky. Balanchine, who’d been a student at the Mariinsky, knew the ballet well, and for many his Nutcracker is the best of them all. A beloved New York City tradition, it is also a tradition at ballet companies around the world. The Miami City Ballet has very close ties to N.Y.C.B. Its founding artistic director was the incomparable N.Y.C.B. star Edward Villella, and in 2012, N.Y.C.B. ballerina Lourdes Lopez took the helm. Sets and costumes for the Miami production are by Ruben Toledo and his late wife, Isabel. —Laura Jacobs