All these suggestions are great, but I gotta say, when my son's were about that age and we first took them to NYC, the absolute show stopper for them was just the buildings themselves. So tall, so close to each other. They were stunned. "Dad! These buildings are bigger than DINOSAURS!" Likewise, food trucks were a new experience for them. Roasted Chestnuts. Hot dogs with everything. Sure. They liked the other restaurants too, but just the raw city was the star. And the crowds! They LOVED the crowds. We worked hard to mask our own caution about the crowds and let them just take in the wonder of so MANY people all moving at once. Of course, they knew they had to stay close to us, but they were enthralled by the masses. Oh, and the street performers. Musicians, "living statues," etc.
I guess what I'm saying is, your 6-year-old may well love the CITY, whether you do anything at all or not. Enjoy!