There are subways in other US cities, but nowhere near as extensive. One-third of all subway stations in the entire country are within New York City itself.
New York City has more subway stations than any other subway system in the world, and that's not counting the non-subway transit (commuter rail, PATH, etc.)
That seems like a pretty hefty generalization.
> I am not sure if we even have subways elsewhere (which just may be my own ignorance showing).
Maybe you should visit nearby Boston, DC, or Philadelphia.
Have you ever seen a movie or TV show which depicted the Boston, DC or Philly metros?
Most New Yorkers you know will not have cars. Most people you know in Boston, DC or Philly will.
Anecdotal stories notwithstanding, New York is the only city in the country in which the outright majority of people don't own cars. (D.C. is a very distant second).