You know your kids best but there are a TON of things to do. Our first cruise was a 4 day with 2 young teens, now we only do 7 days - 4 is just not enough time! On a 4 day there is only one sea day, right? There's the pool, ESPN zone, game room, movies, Studio Sea, organized kids activities, the sports deck on the front of the ship. At CC there is every beach thing you can think of to do from snorkeling to sailing to canoeing to biking. Nassau might be your most boring day - depending on which excursion you book or what you decide to do. It has been 4 years since we did our 4-day and our kids did a teen catamaran excursion.
If your kids are computer nerds, you can rent internet time. I would never do this though - I don't need to spend all that money for my kids to sit in front of a computer!