Depends. State Schools (which NYU is NOT) are cheaper if you live in that state. Private Universities (like NYU) run the gammut. They're up there, though.
a lot are private, but a lot are state schools too. the state schools often have state in them. for example, penn state is a state school, while the university of pennsylvania is a private school. just check out the website for nyu if that's what you're interested in. you'll be able to get the most info from there.
State schools are the ones that charge less for in-state students. If you're from out of the country, I'm pretty sure you just pay out-of-state tuition but you'll probably have to undergo testing in the TOEFL, etc. unless you're going to an American school abroad.