We have done the two hour historical city tour. We booked the first one, right after the ship docked. We were finished early so we had the rest of the day to explore. We (myself, hubby and daughter 22), thought it was excellent. They take you to the Queens staircase, allow you time to climb and explore, there is a light house at the top you can ride the elevator to the top and look out over the island/water. There is a couple of stops at forts, to explore, great views and photo spots at all of these. They give a an overview of the plant life, homes, etc. If your kids like history/exploring I think this would be great for all of you.
Definately, DO NOT, let someone talk you into staying on the ship. Nassau is fun, the people are very nice. Go and enjoy of bit of it. Also, you can let the kids mail postcards back to their friends from Nassau, you can buy the postcards/stamps at the pharmacy, it is very close to the port. Then, just drop them in the big red mailbox. Let the kids mail one back to themselves as well, so they have the postmark for a souvenier.