Recs for Northern Caribbean in November?

[Lisa7]

We are thinking of going somewhere in the Caribbean the week of Thanksgiving. Most likely the Cayman Islands, Jamaica, Puerto Rico or The Bahamas since they are the closest & easiest to get to since it'll be a short trip. We are looking for somewhere for us to mostly relax on the beach, eat good food & enjoy to scenery without spending more than $200/night on a room. We are looking for a non-AI & not a resort. Does anyone have any places that they would like to recommend? Thank you.

[sparty04]

Never stayed there, but someday I will stay at The Rockhouse in Negril. We visited a bar on property last year and it looked fabulous. I've been eyeing it for 5+ years now but AIs keep winning us over.