Non all-inclusive options in the Caribbean?

I'm wondering if anyone has experiences with hotels in the Caribbean that aren't all-inclusive? The more I research, the more I realize that it's important to us to experience local food and culture, as well as to relax on a beach with a drink in hand, swim in the ocean, and go on awesome hikes. We don't really want to be stuck at a resort eating American food for a week – we want to experience the place we travel to. Any suggestions?