Here's a tip...you're going to the Bahamas with your kids..right??..
OK..load 'em up in a taxi and take them with you to the Atlantis Resort and Casino..show them the aquarium and the rest of the stuff there then you park them in a game room while you go gamble in the casino.. then go back to the ship...it's alot more fun for them there.
Of course, you could go to the straw market and shop, which you might like...and which they wouldn't like because of the locals pushing drugs and such and, or take them for lunch at Senor Frogs..(crowded, loud and over-priced..)
One last thing..Nassau is a beautiful island but if you're traveling with kids keep this in mind..
..the water slide onboard would be much more fun..sign'em up with Camp Carnival for a day..it'll be worth it..!!
Hope that helps..