We just returned from a trip to the Dominican Republic, it was a fun adventure and lovely Island to visit rich in history and agriculture and of course famous Caribbean beaches. When we were planning this trip, we knew we wanted to hire a car and drive to explore the Island and then spend the last few days at a resort over Christmas. Mostly for the kids, the beach access and pools are a plus. However we really aren't resort people I found it to be overwhelming with so many people and truly having the car and being able to leave and drive around was magic for me. I can see the appeal and also understand why others don't venture out of them much it takes guts. We drove all around Jamaica when we visited, also Puerto Rico. I asked a few locals about the plan but to be honest I am not sure they wanted to encourage us to drive around and really the beaches are what most folks go for or organized tours to sight see.
Like most of the Caribbean Islands alot of the population live in poverty especially in rural areas and live in simple houses, crime is an issue, traffic can be bad in the cities and you have to keep your wits about you. But having said that I don't think many of the Islands are as dangerous as people feel they are and the fear factor is a benefit to the resorts to keep folks on them.
To truly experience the culture and meet locals exploring is priceless in my opinion.