This is a very common question asked in our office and the answer isn't a flat "yes" or "no".
Most of the time the answer is emphatically YES, because we are firm believers in recommending our clients get out and explore! Beyond the walls and confines of your resort lies a beautifully wild island. Lush and green, though not always manicured, it is a treat to the eyes.
(With a group of travel industry folks on a recent trip to Anguilla at Elvis' Beach Bar in Sandy Ground. GREAT Place! You can find Elvis on Facebook too.)
The local Caribbean people are charming, warm, and friendly. When traveling abroad, we feel it is so important to get out and interact with those lucky enough to call the islands 'home'. This simple interaction helps make the world a better place by breaking down the unconscious and sometimes dangerous stereotypes we all carry towards people from other places.
The only time we advise against adventuring beyond the confines of your resort is if you plan on leaving your common sense locked in your hotel room. In 12 years of exclusively selling Caribbean Travel, the only negative situations my clients have encountered, involved accepting rides from strangers who offer to take them to buy illicit drugs. Would you accept such an offer in your own hometown? Hopefully, not! Its a simple example of the fact that even though you are on vacation, don't take a vacation from your better judgment... follow that tip and you'll be fine exploring all the fun places the islands have to offer! Enjoy!