Unfortunately, the caribbean is a blend of good and bad when it comes to some of the ports and I would recommend for the most part that you try and team up with other passengers if venturing out independently. Road Town in Tortola is pretty safe and the tour along the ridge of the island to Pussers Landing is very scenic. Cane Garden bay,on the other side of the hill is another favourite and if you want to laze on a beach then this is the place to go. Willemstad is good for shopping and if you are interested in its Dutch heritage you will find tours to expand on this.
Hello, I went on my first big ship cruise to the Caribbean on Princess line last year - I like you did not fancy going solo ashore so stayed with the organised tours from the ship; when the sightseeing was over the tour usually ended in a safe shopping area - also by using the organised trips the guides gave a lot of information. Have a good look at the trips on the tour personaliser section and make your choices; I really enjoyed the Caribbean and plan on going back ther next year. Enjoy!