Yes, we just returned from the Destiny out of San Juan. It was a great trip. You don't get much time aboard the ship before you're in St. Thomas the next morning, then Dominica, then Barbados so your first day at sea is the 4th day, so you're quite busy at first if you get off on each island.
Fredos is a wonderful island guide in Dominica. For US$40 per person he'll take you on a 5-6 hour island tour you'll never forget. It's through mountainous tropical rainforest including waterfalls, orchards, plantations, Mr. Nice Fruits stand. It's fabulous--a "must do" day. His website is email@example.com
or freddy536.tripod.com. You'll save bundles of $ instead of taking the ship's shore excursion.
If you just want to "see/tour" the islands without going out in boats/snorkeling just take a taxi tour from the end of the pier. They all have fixed rates -- Aruba 2 1/2 hours, US$20 per person. St. Thomas was 2 hours for US$25 per person I think. They are safe, they get you back to the ship in plenty of time, they go on your time schedule and they save you much money over the ships' shore excursion tours.
Aruba is flat, desert island with cacti. It's worth taking a taxi tour to see the Natural Bridge (which has now collapsed) and Atlantic coast side.
The dinner menu is wonderful in the dining rooms. The evening shows in the Palladium are "must sees". The sea was a little rough from Aruba back to San Juan--pretty common.
We learned you can start the embarking process as early as 1:00 or 1:30 on Sunday. There is a place to store luggage in old San Juan before/after the cruise for $2 per bag so you can "tour" the sites without luggage if you want. It's right across the street from the ship terminal.
Hope that's helpful. Is this your first cruise? Have fun. Feel free to ask other questions if you want. Tina