My experience has been that food on most Caribbean islands is expensive, especially produce, meat, and dairy products. Most food items preferred by American tourists are produced in the U.S.A. and elsewhere. Shipping, storage, and refrigeration add incremental costs. The exception to this may be Mexico and some Latin American countries like Belize and Honduras, which may be large enough to produce many of their own items. But food produced in these countries comes with it's own gastrointestinal challenges for North Americans. A great way to save some money on food is to find accommodations with a kitchen and cook your own meals.
I'm not sure what you mean by "entertainment", as this comes in many forms. For example, we like to scuba dive and prefer to dive from shore at our own pace. So we visit Bonaire for several weeks each winter and pay $150/week, per-person, for unlimited scuba tank rental. Others staying on the same island may pay the same amount for a day's worth of guided diving from a boat. If golf is your thing, you may be able to get 18 holes in for $150 to $175. Sitting on the beach and reading a good book is pretty affordable.