Key West is such a magical place that just walking around is a shore excursion in itself. There's a little train--Conch Train, I think it's called--if you preferred transportation of a sort. Bahamas--Atlantis is something to see if you haven't been there. You can buy a day pass and go on all the water slides and such. Grand Turk I've only been to once and if it's the same port, there's a Grand Turk Cruise Center right there with a Margaritaville, a big swimming pool with deck chairs right there and a small beach. Just a really nice place to relax if you don't want to go on an organized excursion.
Like Polina said, the main draw of Grand Turk is the snorkeling and scuba diving. The Cruise Center has a huge pool and a private beach, although it can get pretty crowded. Governor's Beach by Cockburn Town is beautiful and not as packed. Your teens may enjoy some of the Chukka excursions like dune buggies and horseback riding, but the twins may be a little young for those.
If you're docking in Nassau, Atlantis is a great bet. At Dolphin Cay you can swim with the dolphins in both shallow and deep water, so you should be able to bring the young ones. Paradise Island’s Aquaventure Water Park is also a great family destination. There's also a pirate museum a little bit further inland as well, so you have quite a few options!
Thanks for all your ideas everyone. Much appreciated. We will be having a family meeting this weekend to discuss our options. I also found a Fodor's book on Caribbean ports at my local library. Maybe I'll get more ideas. Lots to plan! Getting excited! I'll let you know what we decide.
That sounds like fun, @wannacruisemore! Definitely let us know what you end up seeing.