Do you want to see real inequality? Do you want to see well-fed people, satisfied smiles on their faces, walking past lines of hungry people waiting in the cold, or in the hot sun? It's not hard to find, here in one of the richest cities in the world: just go to any restaurant that has a line for brunch.
Yes, I'm being flippant. But I'm making a real point: just because you observe inequality in a place does not mean that that place creates inequality. In fact, imagine if you had a magical machine that turned poor people into rich ones, or even if you just had someone who sat at a desk and handed out stacks of twenties. You'd see poor people next to rich people, because the poor people have to go to that place to become rich people. In fact, if you go to some of the places where smug people tell you you won't see rich people stepping over poor people, chances are very good that they're that way because of segregation, like Detroit.
I've been to places with relatively mild weather - Seattle, Vancouver and Albuquerque, in particular, but I'm sure there are more - and people there told me that their city attracts homeless people because the living is easy. You can see the challenge: suppose that your city has a million poor people, and you come up with a brilliant economic development plan that lifts them all out of poverty in a year. What would happen next? A million more people would move in, ready for their chance to escape poverty. Perfectly reasonable on their part.
What's not reasonable is to blame "the city" - its government, and usually its people - for the inequality, as I often see being done to New York. If you see inequality in a city, it could be that the city is making its residents poorer, or it could be keeping its poor residents down over generations. It could be that everyone's getting richer equally, but the rich had a head start. Or the city could be making its poor residents richer, and they then move out or have a low birth rate, and are replaced by poor immigrants.
There are even ways to tell. Look at adults (living anywhere) who were born to poor city residents. Are they richer or poorer than their parents? How does their change in wealth compare to the children of their parents' wealthier neighbors?
I honestly don't know. I haven't looked at that data. But I'm not the one demonizing New York for "inequality."