I don't live in New York City but NYC politics matter somewhat to me
New York city is unique. In a sense, NYC is the capital of "The sprawl," the futurist Rhode Island to Atlanta I-95 megalopolis that extrapolation suggests will continue flowing together.
A uniquely American city... yet unlike the rest of America.
As the traditional capital of American publishing and news and fashion and art, it is like Rome was to the distant expanses of the Roman Empire. Even if you never saw it you always heard about it. Institutions flowed from it.
Today New York is only the capital of the east coast, while the west coast becomes more developed and more westward looking. There is some national coastal divergence there as west coast bonds with Asia and Latin America strengthen.
But even 1/2 of what New York was in the 1920s-1950s is a lot of influence. It is still the capital of our money (always of interest) and still our biggest cultural gateway to Europe.
Many Americans identify with New York, even if they have no wish to ever visit. New York is where you go to make an American splash, whether King Kong atop the Empire State building or planes crashing the WTC. New York is where you put the United Nations... the American city people outside America think of first. Washington D.C. is not central to American history except insofar as the government is there. Americans think of DC as symbolizing the government, symbolizing a formal system of law, not symbolizing America.
So yes, I am always somewhat interested in NYC politics, though I will probably never vote there.