Have you looked at any Personal Navigators to see all the activities offered onboard? There's the kids clubs, movies, shopping (if not in port), the spa, the fitness center. There are usually seminars or workshops in the lounges during the day -- towel folding, cooking, mixology, Making of the Dream. There's Bingo and the arcade is open to all ages. In-room movies if you prefer to hang out in your stateroom.
As PP mentions, they will try to steer around storms when possible, maybe catching the outskirts of it though. If necessary, the itinerary may be adjusted. If you end up with an at-sea day rather than a port stop, they'll add more programs and activities offered onboard for the day. Port stops will still occur in regular rainy weather, and excursions may be held as well if it is not considered unsafe to do so in the rain.
Enjoy your cruise!