A lot of that depends on what you like to do. Personally, I'm very comfortable on St. Thomas. If you just want a beach day, there are cabs to Magen's bay, emerald beach etc. It's very easy to take a cab to the ferry and go to St. John also. But if you want to go on a sailing charter or parasailing, it just makes sense to book it through the ship. You'll spend half your day finding a place to do it, and you'll have to wait until the cruise ship passengers who prebooked have their turn.
San Juan is a very easy walking city. But again, if you want to zip line in the rainforest, book it through the ship.
I've never been to Grand Turk, so I can't help you there!
The ship excursions some times sell out, so if it's something you're really anxious to do, book it early. I think you can also cancel them with 48 hours notice, but check the cruise line policy, as they can vary.
If you're like many of us on this site, you'll quickly go from thinking in terms of once in a life time opportunity, to...I'll do that NEXT time.