Hi Michael,
What a fantastic age to bring your children to Disney World, my girls were 7 & 9 their first trip and their very favourite character meal was Dinner at Crystal Palace in the Magic Kingdom with Pooh and friends. We saw Pooh, Tigger, Piglet and Eeyore but characters are subject to change.
Obviously it depends what characters your girls are into but other favourites have been the Garden Grill in Epcot with Mickey, Pluto, Chip & Dale. The restaurant rotates slowly which my girls thought was fun and the characters were fantastic. Also at Epcot is Akershus Royal Banquet in Norway and this meal is hosted by the Princesses, again they can change but we saw Aurora, Snow White, Jasmine and Belle. We have only ever eaten breakfast here as my children don't like the look of the lunch and dinner food but yours may be less fussy. They also really enjoyed Chef Mickey's at the Contemporary with Mickey and pals.
There is a great page about character dining at
www.allears.net, click dining then on the left hand side is a link called character dining.
I hope you have a fantastic trip,
Jo