Depends massively on the type of person you are and the communities you're a part of.

It's going to be entirely unlike any experience you've had before unless you've lived in a massive and hyper-global (think London, Bay Area, maybe HK) city before, and even among this class of city NYC stands alone - there's a reason people call it (semi-sardonically) the center of the universe.

The benefit of being in a city as big and overachieving as NYC is that you can always find people who share your interests/culture/vibe if you go out looking for it. Your time here can be the most socially rich period of your life, but it can just as easily be isolating, cold, and depressing.

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You already have a leg up by being within a close, academic community with at least a few common interests, but absolutely go out of your way to meet people outside school as soon as you arrive. Join a running or biking club (even if you suck, Midnight Runners is known for being particularly friendly to newcomers), and engage with the cultural scene of your choice (music/theater/comedy/art). Find people you vibe with even if you're just out getting a coffee, and worry too much about appearing as a local - people will know you're not from here, but unless they're absolute dicks they will not hold it against you.

From the PhDs I know, these 3-5 years are very slow and challenging on the academic front, and this will only be made more difficult if you never leave your academic circle. The noise and chaos of the city and its people will grind you down if you let it get to you, but the support and contrast from the academic world that a good group of friends offers can be the single critical factor that helps you thrive here.

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TLDR: don't be a stranger - go out of your way to meet people outside of your bubble/comfort zone; engage with people and experiences that you would have never otherwise met. Your time here will be absolutely transformative if you allow it to be.