Best location in Caribbean to take a sabbatical with family?

I qualify for a 1 month sabbatical and I am starting to do some research on which Caribbean locations I should consider. Since I still have to pay for this I am trying to find the best budget location that is safe and has plenty to do and explore during the month. I also need to consider the travel cost. I am in the Southeast US and would fly out of Atlanta. I guess I am just looking for creative ideas and I am very open to looking at places that are maybe not the most well known. Bonus would be a place that has good surfing, sailing, kite boarding, and fishing. Must have great beaches! I have 4 kids but 3 are college-age so not needing anything too young kid focused. I appreciate the advice.