All-Inclusive Resort w/ Private Pools – Caribbean

Hi there! My fiancé and I are planning our honeymoon and we are looking for recommendations for all-inclusive adult only hotels in the Caribbean. His only request is that it’s a room that has one of those private plunge pools that you can walk out into. I’ve been seeing some good options in St. Lucia and Mexico but would love some recommendations for that ultimate luxury/romance experience. Our budget is flexible!