My kids aren't picky in the usual ways, so their favorites were the signatures and other places with more interesting/varied kids menu choices. California Grill was a particular favorite with all my kids when they were little, mostly because the service is very family-oriented. From goldfish crackers with the bread course to waitstaff that suggest Shirley Temples and add extra cherries, to a pretty good kids menu and one of the best kids desserts on property (rice krispy-and-fruit snack sushi), it is probably the most kid friendly of the signature restaurants.
As far as theme goes, they really liked Sci-Fi and Coral Reef. Teppan Edo was a favorite until we got a teppanyaki restaurant somewhat close to home and the novelty of the cooking style wore off, and they've always liked Ohana (which I don't actually love, because I'm not big on meat-meat-meat).