My son and I have done the exact trip you're describing twice, in 2009 and in 2011. We left San Juan for a week cruise to the same islands you list, and we dove at every stop. I would recommend:
St Lucia is the best diving of the islands you list. And we used Dive Fair Helen both trips. They picked us up, drove us about 20 minutes to the dive boat and shop. Brought us back to the cruise ship afterward. Very easy.
The other islands were all comparable for diving... which is to say warm, clear water and so-so scenery. If you can't dive St Lucia:
St Thomas we used Blue Island Divers both trips. Small boat, only 6 to 8 divers, picked us up right at the cruise ship dock. We even watched the other shop load the cattle boat for the divers that booked through the ship... and then we took off. And at the end they took us right back to the dock (literally, pulled up right in front of the cruise ship.)
Barbardos... very convenient since the cruise ship dock is right next to Bridgetown. We used Barbados Blue for the last trip in 2011. Their shop is in the Hilton on the southern side of the harbor (the cruise ships dock on the northern side of the harbor.) Loved their boat and the crew was great. Diving was ok.
St Maarten... we went out with Scuba Fun. Their shop is a short walk (5 minutes?) from the cruise ship dock. As with Barbados, great people, ok diving.
Antigua... we only stopped there on the 2009 trip. We went with Jolly Dive, run by an older British couple. The husband was our guide, must have been over 70 but it didn't slow him down. Great guide and operation. I don't remember anything particularly memorable about the diving.
That's all I got, and I hope it's some help. Basically St Lucia is the best for scenery, and I haven't found a dive shop yet that I'd avoid. Good luck!