Fancy Free - ballet - was created in 1944.

There is not one that is the best but there are many amazing ones. Canada's National Ballet School, American Ballet Theater, Royal Ballet School, Paris Opera, Australian Ballet School, Houston Ballet School, Stuttgart Ballet, and the list goes on....

I'm 90% sure there isn't an official list. But for international companies, they have what they call the "gold standard" list. This list includes includes the Kirov, Bolshoi, Paris Opera Ballet, Royal Ballet, Royal Danish Ballet, and New York City Ballet, in which case NYCB would clearly be among the top 15 in the US. But for the others, a list of that sort would most likely just cause a lot of arguing.

Though the 1944 San Francisco performance was the first time the ballet was presented in full in the U.S., the music wasn't new to Americans. The ballet debuted in 1892

There is no official list.