Winter Vacation suggestions: we want to walk on the beach, but not in Florida.

We are in New England and tired of the dark and cold. I don't like resorts where they play loud music by the pool and people drink too much, although we like to swim in warm water. We are not interested in Florida. We wonder about Puerto Rico and Caribbean islands. We have passports. Not looking to be extravagant, but also looking for something quiet and pleasant. We like nature trails and good food, might consider snorkeling. Any suggestions?