Having lived here for a year and a half now, I think that the Chicago experience is actually more quintessentially American than New York City is. NYC is amazing, don't get me wrong, and in many ways it's what the US aspires to be. There are still parts of the city where you can move there from, for example, Ukraine and never speak a word of English. For the tourist, this is also a neat experience where you can hop on a subway and go to Little Ukraine or Koreatown or Spanish Harlem and experience some vastly different cultures within 15 or 20 minutes of each other. There's so much you can go to on NY that are world-renowned cultural landmarks, from the clubs that Hendrix and Dylan played at to the grave of Alexander Hamilton, from the special kind of showy street basketball they play at Rucker Park to the whole apparatus of Broadway. And yeah, there are a ton of cheap eats and if you're willing to live in a bit of squalor you can live poor in NYC too.
But I feel like there's no in-between in NYC. You either live in Manhattan and make 7 figures or you live with 6 roommates. Chicago, on the other hand, has the in-between where you can earn a 5 figure or low 6 figure income and still not feel like you can just barely make ends meet. Also, while NYC is what the US wants to be I feel like Chicago to a great extent is what the US *is*. It's a bit on the racist side, the crime rate is really, really high in a couple neighborhoods (though I will say, if you're not a gang-banger and you're not walking around alone in the middle of the night in these areas, you're still not terribly unsafe), there are sometimes major divides between rich and poor. I've seen Chicago cops do some things I've never seen cops in cities like NYC or SF/Seattle/Portland do and I don't mean that in a good way. But it's also *so* underrated... yeah, you get the second run of Broadway shows here, but if you like live theatre there are a *ton* of shows here and a whole Broadway-like district to see them at (creatively called the Theatre District). Chicago may not have the iconic Macy's with the wooden escalators like NYC but it does have the Macy's that used to be a Marshall Field's that is iconic in its own right and besides, if you want iconic shopping there's the Mag Mile. NYC has Saturday Night Live but Chicago has Second City, the venue that creates like half the people who eventually become SNL players (the other half come from an LA-based troupe called The Groundings). NYC's varied ethnicities mean it'll always be the best food city in the USA but Chicago is a damn, damn close second, and it's a close second on its own terms.
So yeah, I know this was a question about NYC but dammit I know Chicago and Chicago is kind of awesome.