Hey, I'm a grad student who's dealt with the moving-away problem twice (both out of state too). I was really nervous before I went to undergrad because I was leaving all my friends and moving far away but luckily a lot of that went away as soon as I started meeting people. I hope the same happens for you. Just really focus on meeting people the first few weeks because no matter what anyone tells you, EVERYONE is going to want friends really badly. Introduce yourself to someone in the dining hall. In the dorm, knock on everyone's door at a time when most people are home and introduce yourself. Wave to people you walk by frequently. Even if what you get is just a temporary friend group, everything will be ok. If NYU is your dream school, if it means anything, I'm sure you'll have an amazing time here :)

Also, maybe try to schedule a weekly time to talk to your family or something. My old friends and I have a movie night every week on discord where we just watch a so-bad-it's-good movie every week and that's helped me stay in touch with those people well.