We loved the pirates museum at nassau. I believe it was $12 per person. You do it on your own. It is a large purple building 2 blocks behind the straw market. a short walk from the pier.
The dig (aquarium) at Atlantiis was good too. The tour goes quickly, but you can go back through on your own as much as you want after your tour is over. Just show your bracelet they give you. You can do this on your own too. Just grab a taxi at the port, not sure of the price, I think it was $7 per person, one way then the price of admission to the dig, not sure how much it was. Don't bother with the glass bottom boat tour, it's not worth the money. saw a couple of fish and a sand dollar, that was all and the weather was windy so we couldnt go and see the shipwreck either.
If your into history the 2 hour historical city tour ( can book at the pier) is an excellant tour. We saw 2 forts, queen anne's staircase and a few other things. One fort was a guided tour, the other you just walked around yourself. But the guide has a lot of interesting history about each spot, a kid might get bored, i dont know. each person is different. But for the age of your kids I would highly recommend the Pirate museum. watch out for the pirate who greets you, he seems to like watches and rings etc... he was great!!!