...that you need to consider.
Any of these islands have lots of good places for new divers to try, shallow and protected is probably what you are considering.
On St. Thomas, contact Sean and Aitch at Blue Island Divers in the Crown Point Marina and dive with them. One of their (an my) favorite dives is the Navy Barges, in the middle of the harbor. The water there is pretty protected, and only about 40' down. There are swim throughs and lots of things to look at, as wells as plenty of sea life. This is a good dive for a new diver.
I really like to dive in St. Thomas, and cannot recommend Blue Island Divers highly enough. They have a nice shop, a cool old boat, and when I was there on a cruise ship in January, actually came out to the cruise ship pier and picked me up with their dive boat. Wanted to help me rig my gear, really made it a very nice experience.
Actually, I'm looking to get back to St. Thomas to do some diving in a year or so. Charlotte Amalie is a nice town and has lots of things to do other than dive.
When I was on my cruise last January, I dove with Dive Safaris on St. Maarten, who picked me up at the ship. Never did go into town, just dove and then sat at the little tiki bar on the pier afterwards and had a couple cold ones.
On St. Lucia, we did an island tour and I didn't dive.
On Barbados, I dove with Blue Reef Divers. They came out to the gate of the cruise ship pier and picked me up and took me to the shop. You leave from the beach in front of the shop and dive from an island built wooden boat, and do a back flip entry off the gunnell.
I told you about St. Thomas. That was the best of the three islands that I dove on that trip. Can't speak for Antigua, never stopped there.
Hope this is a help! Drop a line if you have specific questions.