A few reasons, some of which have been touched on. A lot of these apply to all cities, not just NYC.
Space. There's not much of it in NYC. Well there is some, but skyscrapers are on top of it. As someone who grew up in suburban/rural PA, it's easy to take it for granted. During recess, we were able to go outside, onto the field, and play football. In New York, there really isn't a field. It's all blacktop. And it's cramped. There's a reason that stickball is a thing in cities, whereas everyone else plays baseball. A basketball court is a lot smaller than a football field. You can fit at least 3.5 regulation basketball courts on a football field.
Culture of different sports. People grew up playing basketball, so it's passed on to their kids. It's like people in the northern midwest playing hockey.
Cities have more available entertainment. In places like West Texas, high school football is a religion. Friday Night Lights and even The Rookie have shown this. A main reason for this is that there isn't anything else to do in places like this. Kids don't have any other activities, so they play football, and there isn't anything for adults to do, so watching football takes precedence. Hell, you've seen Rudy. In the middle of Indiana, all there was to do was watch Notre Dame. This is a main reason why places like LA don't have an NFL team and Miami is considered a bad sports town. Because they have an abundance of activities, so they don't really care all that much about sports in the first place.
Education/Politics. NYC is very highly educated, and very liberal, two demographics of parent's that [don't let their kids play football].(http://www.nytimes.com/2014/11/04/upshot/football-the-newest-partisan-divide.html?abt=0002&abg=0) As a result, less kids are encouraged/allowed by their parents to play football growing up, leading to less players.
I think it's a combination of these 4 factors that explain why NYC doesn't produce top football talent.