I hit all of three of those ports on a Panama Canal cruise last fall. I have also done quite a few shore excursions of all types, and it pretty much comes down to a question of what YOU enjoy. Princess's shore excursion program is one of the strongest in the industry, so there are not very many "losers" in it. Princess also goes to great pains to make sure that the descriptions really are accurate and to update them as tours get modified, so they are pretty credible -- but do read them carefully and make sure you understand them. Also, believe the icons that indicate the level of physical activity that each excursion entails!
All three of the ports of call that you mentioned have excellent shore excursions.
>> In Aruba, I thoroughly enjoyed the "Catamaran Sail, Snorkel, and Beach Barbecue" -- a great day of "fun in the sun."
>> In Dominica, the "Grand Tour of Dominica" is a winner.
>> In St. Thomas, I highly recommend the "Champagne Catamaran Sailaway to St. John." It's definitely worth every penny of the price. I chose this excursion for the third time just last Friday, and I'm ready to do it again!
Have a great cruise!