New york city

There are 8.491 million people living in New York city. The number was astounding when I first read it. It is the most densily populated city by far from other cities that have a large metropolitan areas.

A couple of questions to ask.

What is New York city influence in the culture of America? Food? Travel and Fashion?

Where does New York city rank among other cities in the world? Its municipal structure?
Why do business and corporations pick a large city like new York to place its headquarters?