I can only speak to Tortola and St. Maarten. I'm not sure that there are any main attractions that are a "must see". As mentioned above, the French side of St. Marteen is nice to go see (but could be far depending on where you dock).
I've heard numerous people tell me that you can save a lot of money by avoiding the on-ship packages, and just finding a taxi driver when you get to land and negotiating a rate for him/her to take you on a narrated tour of the closest and most interesting things to see. Tropical gardens are easy and interesting to do in a couple of hours, which is about the most you want to spend at any given attraction given you're only there for a day.
Perhaps the best suggestions would be to do some diving from the Turks. If you're not scuba certified yet, you could get your class room and pool sessions done now, and do your open water (in ocean) dives when you get to Florida. MUCH better than snorkling!
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