Lincoln Center is one of the hubs of the performing arts in New York City. With opera, symphony and balle in residence and a regular selection of guest companies and special events, as well as a great threatre, a film festival, julliard and the performing arts library -- this is ground zero for the more classical performing arts in New York City. Stop by, pick up some brochures and figure out what you want to see. It can be pricey, but it can also be affordable. They also have great programs for introducing children to the arts.
Also you know that red carpet Nicole Kidman walks up in the Chanel ad? That set-piece is based on Lincoln Center.