I've always wondered: what are school buildings like in New York?

I'm used to south-western michigan where schools are generally built on a plot of land outside the city so that they can be single story structures made of corridors lined with class rooms stretching in every direction, generally with a gymnasium / cafeteria / office area functioning as a hub surrounding this is usually a parking lot (small for elementary schools and middle schools, but much larger for high schools) and other land dedicated to general purpose / sports related activities.

I've always had trouble imagining what changes would need to be necessary to fit the equivalent in a city such as New York.