When you get to Dominica, there will be lots of tour guides right there at the port waiting to show you their beautiful island. Expect to pay around $30 per person for a tour. If I had to choose between the Emerald Pool or Trafalgar Falls, I would go to the pool. The two are quite a distance from each other but it is possible to see both in one day. Either of the two will require walking up and/or down a trail. Mr. Nice's Fruit Stand is another very popular place. He doesn't sell anything, just asks for donations (look for the coconut hanging from the ceiling), and the fruit he offers is just incredible.
Depending on what you want to do on Barbados, and how adventurous you are, I've heard that the Boatyard is a nice place for beach fun. We've always rented a vehicle and explored on our own. OUR "must see" places are Crane Beach and the North Point. The Crane is on the east side of the island, so it's not your typical "tropical island" beach, but for me there's just a "feeling" there. At the North Point you'll find the Animal Flower Cave (honestly never been in the caves), and some of the most spectacular cliffs with the waves crashing just like on (I'm going to date myself here
) Dark Shadows.
Check out our photos from the 2006 cruise.
The safes on the Destiny are the card-swiping type.
Haven't been to Antigua or the Dominican Repbulic, so I can't help there.
Now, just go enjoy yourself. Happy Sailing!!