The Cape May Cafe does a great character breakfast buffet that kids seem to enjoy. That restaurant is located across the lagoon at the Yacht Club.
I'll be honest, the only restaurants I've been to on the Boardwalk side are (1) Flying Fish Cafe, (2) ESPN Club, and (3) the corndog cart out on the Boardwalk.
Flying Fish is awesome (easily my wife's favorite restaurant at WDW, although I hold a special place in my heart for Shula's and California Grill). Still, it's not really a kid place, although I've seen kids there when I've been before. The ESPN Club is cool if your kids like sports.
I also highly recommend the corndog cart and the funnel cake cart if you enjoy the experience of hearing your arteries clog with grease.