I completely agree with Maineac.. Vieques is a state of mind. I lived there for a couple years back in the mid-1990s. You will definitely have people from New York in abundance, both residents and tourists. If I could talk my wife into it, I would move back to Vieques in a minute.
Yes, the pace of life is slow.. you are on Vieques-time
I brought my wife there for 10 days a few years ago, and we rented a cottage at Evamer, on the north side of the island. Although we went into Isabella Segundo and Esperanza for most of the daytime hours, she did find herself a little bored. I took her through my old base, we visited Red, Blue, and (my favorite), Green Beach, we drove around the backside of the mountain, but it wasn't enough to hold her attention for 10 days.
Regarding opening a business, I think it would depend. There are many people who relocated from New England/New York and opened stores and bars. Bananas was always my favorite (along with Lazy Jack's), and it is owned by a Massachusetts native (or was, the last time I was there).
The problem you may run into with a new business is traffic. There are already enough bars, boutiques, scuba outfits, charter boats (and planes), grocery stores and markets, restaurants in all price ranges, etc. I think you'd have to find a niche.
Overall, Vieques is my favorite location in the world, and I've traveled extensively. But, if you haven't experienced it yourself, I would 100% recommend flying down for a few weeks. See the ins and outs. Grab a Medalla and sit on the malecon. Do that for an entire day, as that is life on Vieques.
Good luck!