I hear you talking!! We got a good last-minute package deal in Jamaica last summer, at the Riu Ocho Ríos. That is a good base in the country if you are interested in daytrips. The hotel is nice, and has an adults-only deluxe wing that was very calm, chic and not particularly lovey-dovey (although you will see honeymooners having a moon/candlelit dinner down on the beach under their own awning). I booked with Sunwing and for the second time with them, I was a happy customer. Jamaica is perfect for just lazing around by the pool. I too have travelled in many poor countries, but the poverty in Jamaica was somehow more depressing. For the first time, I really didn't want to venture outside the plush hotel complex. So while I felt existential guilt about being well-off in a messed-up world, I didn't feel guilty about not running around trying to see sights.
I did not feel this way about the Dominican Republic. I went there twice, once with the family to a Punta Cana resort and more recently on my own for work followed by a weekend of R&R at the secluded and aptly named Casa Bonita in Barahona, in the western part of the country. The captial, Santo Domingo, is well worth visiting too for its fine architecture, cultural scene and dining. I think DR has the prettiest beaches. The country is quite safe compared to others in the region, and I felt perfectly comfortable walking around the streets on my own and chatting with the locals.
Another good Caribbean destination for a mix of culture and poollife is Panama. We stayed at the Decameron Playa Blanca which was vast and sumptuous. The resort welcomes and caters to families, but the kiddies didn't overrun the place (or maybe they did but we didn't notice because we had one too) and there was a definite fashionista vibe throughout as well as an adult-only pool. The beach there wasn't as pristine as DR beaches, but certainly pleasant. Panama City and the canal are definitely worth stopping off at for a couple of nights.
Enjoy your alone time!