Good luck to you, OP - glad that you are moving for a job because I'll assume that means you'll be able to afford the expense of NYC. I lived there for 55 years in Manhattan, Queens, Brooklyn and, as a kid, Long Island.
Very close access to music generally means a popular area, which always means expensive. Luckily the subway connects everything, so if you can deal with the timing, inevitable delays and crowding you can access areas fairly easily. But there are always crowding and delays. Always.
I've read others mentioning Staten Island and other more outer borough locations, which are fine in themselves I guess but will impact your ability for easy access. A car can be very problematic depending on where you live, and almost always involves moving the car to avoid costly tickets, towing, boot. My last apartment was in the Brooklyn neighborhood of Ditmas Park, and I can say it was the only NYC area in which I ever dreamed of owning a car (didn't have/need one for about 40 years of my adult life)-yet in Ditmas I was able to own a car with minor (tho constant) inconvenience when it came time to find a spot. This is worsened, tho, at 3 am when you need to find a place to park after a gig and all the cars in the neighborhood are firmly in place for the night.
Yes, no car will mean you will have issues moving an amp, but they invented lightweight combos and taxicabs for that. As far as owning a car opening opportunities to earn a living at your music ... well I GUESS so … but can say that in a lifetime of gigging that possibility never presented itself - tho I sure tried

. Maybe it was the car or lack thereof.
PS: I finally fled NYC for good about two years ago. If I would have known sooner, I would have put in a good word for you with my landlord.