If you haven't already been to Atlantis, I'd say its worth it. We did a ship tour that also included a harbor tour for around $25. Just to get in there and see the dig and the aquarium is something you don't want to miss. Although that does not included their water park, you have to actually be staying there to use that I think your boys would love seeing all the fish.
As for the weather, as long as there are no major storms around, should be plenty of sun and very warm, enjoy!
I believe there are day passes available for the facilities at Atlantis. I also understand
they are expensive. I read somewhere of a family booking a room at the Comfort Suites accross from Atlantis for the day. Apparently guests at Comfort Suites have use of the facilities of Atlantis. I don't know what the prices are, but it might be something to make a call or two about.
Enjoy your cruise.
I was in the Bahamas years ago and we did the tour of the town. It was nice. There was a tour of the Fort Charlotte. It would really be neat for the boys. We also went to the water tower. It is the highest point. You can see forever. Really pretty. Have a great time. Char
There is a great pirate museum that can be easily walked to from the cruise dock. It is really fun and your boys will love it! Bring money for souvenirs; they have a great shop with replica flags, eye patches, hats, coins, and other pirate fun stuff. There are discount coupons printed on the Nassau downtown maps that are available for free in various locations--just look for them. Allow up to 2 hours to play here. Bring a camera for shots on the patio area of your family, they have a few props you'll want to take pictures of your family in.
You can have a garden burger with fries on the patio also, and there is a full bar. Prices are reasonable to slightly high.
If you go to the museum you would still have time for Atlantis, and that would be my second recommendation. Or take a Robinson Crusoe day cruise to a nearby island and go snorkeling, have a great lunch, lie in the sun on the beach. If you do this, rush to the beach ahead of the crowd. Grab a shaded spot fast before others. The tables under the shaded roofs will keep you dry in a sudden down pour. Be sure and snorkel or walk to the right (if you are in the ocean facing the shore) for a secluded beautiful beach just around the point. (very close).
Atlantis and the dig would be just great for the kids as well as mom & dad. We did this on our own; taxi = $4each one-way and tour of the dig/aquarium only is $25 each. There is no total facility day pass. In fact the security is very tight and you will not be allowed to roam the hotel guest pool/beach areas. Thus your son will not be able to use the Water slides. You can walk around the inside of the hotel and "some" outside areas but they are trying to protect their guest.
I'd recommend Atlantis. They'd probably enjoy the pirate museum too. It is a small museum and you'd still have time for Atlantis. Other than that, there really isn't much in Nassau. We'd stayed at an all inclusive resort there a few years ago. It was great! We went with another couple and I told them there was no reason to leave the resort. Just to satisfy their curiosity, we went into town one afternoon. We only stayed a few hours and returned to our resort never to leave again until time to go home. Nassau is mostly shopping aside from the Pirate museum and Atlantis. Try to avoid the straw market. That is where the people will bug you, bug you, bug you to buy their wares and they make up the prices as they go along. You can bargain with them though. The kids might get a kick out of just seeing it. But other than that, the straw market is pretty unpleasant.