There's lots to tell about NYC---especially the Borough of Manhattan.
I would say one thing: New Yorkers aren't as rude as the stereotype. Usually, they might seem rude on the subways because they have to rush to get somewhere. If somebody misses a train, that might mean they're late for their job and (a tiny chance) they might get fired. People are tense if they feel like they're going to be late.
These days, most of the people who "speak" New Yorkese live in the outer boroughs, or in nearby suburbs north, west, and east of the City. South of the city, people seem to have generic Jersey accents, or Philly accents.
I live in the Borough of Queens. There are some museums there--but it's mostly residential.
In Brooklyn, there are museums, and other historical highlights. Parts of Brooklyn are becoming like Manhattan and price and in atmosphere.
The Bronx has nice areas in the northwest section. There's lots of nice old apartment buildings. I find it to have lots more space than other parts of NYC--some of the streets are quite wide, for instance. Still, there's still lots of poverty there.
Staten Island is part of NYC. For the most part, it's pretty suburban.
The area of NYC is about 300 square miles; its population is about 8.4 million.
The Metropolitan area population is approaching 20 million. This includes parts of the states of Connecticut and New Jersey.
The whole state of New York is approaching 20 million, actually. It's now only the 4th most populated state in the US. Florida just moved into 3rd about a week ago.