I'm going to Aruba, Dominica, and St. Thomas aboard MV Sun Princess early next month so I'll post comments when I return.
In St. Thomas, I highly recommend the "Champagne Catamaran Sailaway to St. John" in spite of the $96 price tag. It's worth every cent of that price! The catamaran picks you up right at the pier and takes you to a rather remote beach on St. John. There's also a reef for snorkeling nearby, to which the crew will direct you (and they also provide lessons for those who don't know how). The crew also serves a cold buffet lunch, which is always fresh, while the catamaran is anchored at the beach and they serve beverages (including champagne and rum punch) throughout the whole trip.
Aruba you can go on your own to Palm beach by taking the town bus ($2 pp) and get off near the Holiday Inn. At the beach bar they may even rent you a chaise lounge. The only ship tour I could recommend would be a half day island tour taking in the Lighthouse, the Natural Bridge and Baby Beach. In Venezula, only take a ship's tour into Caracas. It is not a place you wish to travel on your own. At Grenada, just take a water taxi right there at the pier to the beach. Very reasonable and crafts and spice vendors are available on the pier and strolling the beach. St. Thomas you can take a taxi to Maegen's Bay and return into town for shopping or as previously mentioned, take a tour to St. John. If you have never been there, St. John would be my first choice. You can shop right at Havensight Mall at the pier if you need to shop!
Just returned from a wonderful week aboard the Ocean Princess. I would recommend the ship's tour into Caracas to get a flavor of the country, but not for shopping. Grenada tour also gives you a great feel for the island. St. Thomas shopping can be done at Havensight Mall so you can spend time at Maegen's Bay beach - beautiful - or visit St. John. I wouldn't tour Dominica if you've seen Grenada - very similiar. Don't forget to save some time to just rest - we found ourselves on too many tours and cancelled Dominica's. Enjoy your cruise!