I spent a lot of my time staring at the heart of the city from the top of the Google building. The view is amazing there, and I enjoyed a few peaceful moments.
The true heart has to be Times Square. There's just so much going on there all the time. So many interesting things to see.
The New York skyline. I've heard people talk bad about the abundance of brick buildings in Manhattan. I thought it was quite a unique feature of the city, in a positive way. The brick buildings in New York seem sturdy and robust, whereas London's brick buildings seem horrible and old.
You'll note that I did not include a photo of the statue of liberty here. I did take some, but the statue is so far apart from the center of the city, and so far apart from people's daily lives, that I do not consider it to be part of the New York experience. If anything, it's just a stupid tourist trap. I found it very disappointing. The New York - well, Manhattan - that I experienced stretched from the financial district to central park. That, to me, is New York.