Best Island for solo travel

hi all –

What island in the Caribbean would you recommend for a solo traveler? I am taking a year to travel around the world and have a 10 day gap in my schedule during which I am considering visiting the Caribbean. Some quick facts:

– I am a gay while male in my early 40s, pretty active. While I am not interested in any place hostile to the LGBTQ community, I also don’t need a 10 day gay party.

– As I said, I’ll be solo. I am pretty good about meeting people, but maybe this would be easier in one spot vs the other? I also don’t mind – and in fact want – to spend a nice chunk of this alone. A pool and a hammock and an island breeze sounds like heaven.

– Fine with a resort, but I’m not really an all-inclusive guy. Especially when alone. I’d be fine with a hotel, but more than likely would want to do an airbnb.

– I would most enjoy a nice mixture of adventure days and pool/beach days, with the chance to eat and drink like a local.

– I need the destination to offer direct flights to NYC, preferably JFK

– I don’t have to spend the entire 10 days here as I could likely extend by a couple of days the desitnations ojn both sides of this gap.

Thank you much for your suggestions. I hope I can visit the Caraibbean soon!