A one-day-per-island cruise isn't the best way to get many dives in. Check thru the cruise lines as to how much the dives cost, and what the cost is for 'resort' dives (uncertified) vs. certified.
Of the islands listed you're not going to get 'cage diving' in any of them to my knowledge. Visibility is probably best in St. Kitts, St. Lucia, Antigua, Barbadoes, and Dominica, and can be so-so in PR. Dive depths are probably shallower in St. Kitts, Barbados, and PR and possibly Antigua and St. Lucia as well. Dominica and I think St. Lucia tend to 'deeper' dives for the good stuff. (by 'deeper' I mean 60-90 feet, not > 100 feet). So that also influences your choices since 'resort' dives are usually limited to shallower depths like 30 - 40 ft.
In all it depends how interested you are in diving. Do you think it's somethign you want to pick up and the cruise is just the first opportunity, or do you just want to because of the cruise? If you want to 'dive' for real, know that usually the cruise-ship trips due to time limitations and 'consistency' of the offering don't get to see the 'best' sites at any particular island, so you might be a little disappointed if you're expecting National Geographic like views. On the other hand, if you just want to try it out, doing a resort dive on a cruise is probably not the worst way to try, as you do have several islands to choose from and usually the cruise lines won't give the local outing contract to some fly-by-night operation if only out of the interest in avoiding liability.
Maybe rank islands in order of how 'good' you read the diving is - then counter-rank them based on how interested you are in topside experiences there, and pick the best one that pops out of the bunch to dive on without sacrificing a good island day. If you're only spending a day per island I can't see you really wanting to dive EVERY day...kind of ruins the point of the cruise?
p.s. I've dove Dominica (loved it), St. Kitts (enjoyed it but no candle to Dominica), and snorkeled in PR. Others I am only guessing somewhat from what I read around various scuba trip reports and the like.