Keeping it local on a rainy day. That leaves out Friendly. Rainy days at the Naz is not too bad when they can hop in the water between spells. Town Docks a bit far out but it can get a little humid and hot inside the building if raining.
T-Bones/Cactus Jack is very kids friendly but not much activities to keep them occupied. Food including the kid's menu are great. Kids don't see anything they like? The staff does a tremendous job fitting their taste if its not a menu item such as PB&J sandwich!
Griddle in the Middle was a success for breakfast, unfortunately it is close.
Funspot can get expensive so try
Jumpin'Joy on Rte 107 in Laconia!