Nassau - Weather was awful. The ship cancelled many excursions. We booked a room directly with Atlantis (best option for family of 5) so we decided to go for it. The Dig aquarium is amazing. Weather managed to clear enough for us to use waterpark which was great. Best lazy river I've ever been on (it's like white water rafting). Kids water playground was their favourite. With the not ideal weather, there were no lineups and it wasn't too cold. When my 4-year-old did get cold, we brought him to the hot tub. Tip: Food is extremely expensive. We got 5 sandwiches and 5 drinks, it was $105. No joke. I recommend bringing a box of ziplock bags. It could have been much worse if i didn't bring some of my own snacks. I went to breakfast buffet (Cabanas) and grabbed 3 boxes of Fruit Loops, then loaded some muffins in one bag, croissants in another, pancakes in another and then grabbed two bananas and 3 apples. I couldn't bring drinks unfortunately but if you have drink boxes, do it. They don't check your bags when you come off.
Castaway Cay - Disney thinks of everything. I recommend taking a photo when you get off with the family with the Dream in the background. Strollers here aren't necessary unless you need to nap a little one. The tram comes every 6 minutes. I thought food was great. Beach was terrific. Fish are hard to see if you snorkel but they are there. My 4-year-old managed to see them swimming at his feet.
There were lots of beach chairs available and umbrellas. No need to really do any kind of excursion on this island. Just enjoy the wonderful beach.
They do have a kids club on Castaway Cay too but we didn't use it.