> Is a ballet school for rich kids part of a creative scene?

Yes? And it isn’t a school, it’s a repertory. With performers—not kids—from a variety of backgrounds.

Next to the promotional events (which aren’t always horrible) you will find publicly-funded music performances in the park (I never go to these), lectures at NYU and the New School, and random local performers at several bars in the neighbourhood. (Though I personally prefer the West Village for jazz.)