I just did this cruise on the Miracle!
I went to the Bohio dive resort in Grand Turk, took a taxi, much nicer beach then the one the ship docks at and plenty of time just time your cab ride there. Or you can take a taxi tour to the Lighthouse and around the island. Not much to see and do on Grand Turk but the space capsule was neat and I got to see some pretty horses roaming.
In La Romana I did Carnival's tour to Santo Domingo well worth the bus ride it was fascinating and the "real" Dominican Republic, we saw the oldest churches in the America's, beautiful paintings on ceilings like in Rome, the giant Lighthouse shaped like a cross where Christopher Columbus is buried, the place where Columbus son and family lived. There are two tours we did the long one that included lunch, food was decent.
In Aruba I did the Jolly Pirates snorkel tour, I regret not going on an island tour, here, as water was really deep and choppy. I stayed on the boat.
In Curacao we did the Double the Fun Tour with Carnival and it was one of the best tours I've ever done. We saw Boka Tabla where the waves crash, took amazing photos, went to two pristine beaches to take photos, went to two museums, and the the Liqour factory for tasting. Never did we feel tired or bored on Carnival's long tours they were great! Hope this helps!