The best solution for you might be a visit to New York to do part of a certification, but you will then need to pay for instructor time on your holiday for 1-4 dives until you become certified.

There are 3 ways you can dive (similar across different organisations subject to a few differences in words):
OW certified: Means you can dive with any other certified diver and you basically have the skills to look after yourself. This is the traditional "diving certification" It will take 4 dives in real water, a couple in a pool and most of a day of theory. This might take 3-4 days all in, or you could probably squeeze the theory and pool work into 2 days in New York before your trip
Scuba diver: This might be a viable option for you. You'll do half a day of theory and a bit of pool work before you go in the water. You're able to dive with qualified instructors/ other diving staff from then on and can probably roughly get around underwater and enjoy yourself. I'd recommend going full Open Water if you can, but if you just want to be able to get your head under water and go diving with local guides this could be enough
Discover Scuba Diving: This is the basic get some theory, practice in a pool and hop into the water as soon as you can. This is just a once-off experience and would be something like academic and pool work and then you're on a real dive a few hours later. You will be able to get underwater but unless you're in beautiful water you'll have your instructor holding onto you at all times and you won't have the same kind of experience as a qualified diver.

Or you can just jump in the water and go for it, but you stand an unreasonable chance of getting killed in an accident if you do. I'm a PADI Open Water Instructor and there are no shortage of stories out there of people who have cut corners and suffered the consequences.