In San Juan,you could tour the forts, visit the Bacardi Rum Factory, do an island tour, shop on Fortelza St....
In St. Maarten, make sure you visit the French side..Orient Beach, [parts are nude] & Dawn Beach are nice...up for some adventure? Do the America's Cup excursion.
Check out what the ship offers...most you can do on your own and save money.
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Trip, with her book & tea!
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Have a look at all the excursions listed by the cruise line for the various ports of call. Then go to Youtube and see videos that cruisers have made. Some will be cruiseline sponsored tours and some independent, but you should get a good idea of what interests you.
On St Martin you will dock in Phillipsburg, from the pier you catch a water taxi over to the town ( or walk for 20+mins) where you can shop, then you can get a taxi to beaches for around $20.