There's plenty of stuff to do. Check your Navigator, though, I have never had it rain all day (in 12 cruises) to the point that you had to stay inside all day. Be prepared, though, you most likely will hit a rain shower here or there in the Caribbean. Usually quickly moving weather systems (unless we are talking Hurricaine on the horizon), that blow through within a couple hours or less.
We ran into a worse problem on a cruise to Mexico & Honduras, The seas were very rough for the last 2 days of the cruise, both of which were at sea. We had 20 ft swells for the entire 48 hours, but the weather outside was sunny & Hot, Hot, Hot (about 98 and humid!). Problem being......closed pools! The pools were so rough that they had to close them due to the safety of the passengers (I mean, the pools were virtually empty and the water was splashing out about 6' high.) Great fun to watch! So, unfortunately, it was way too hot to stay outside in the beating sun without a pool to relax in, so everyone spent the last two days at sea in the air-conditioning. Luckily for me there was a casino. We played bingo, shopped, had quite a few cocktails in the lounges, I believe we did a wine tasting, had a little "alone time" in our cabin-wink, wink. We don't do movies on a cruise, but that's always an option. We did an extra spa treatment (glorious). If I remember correctly, we had a blast just winging it.
Mrsfuzzmo