I have DS 6 and DD4 and have been going to Disney since they were babies. Here is a list of the spots we enjoy:
*Ohana - Delicious. PLus they have activities for the kids like limbo, pineapple races, and dancing
*Garden Grill - character meal served family-style. Good food and if your kids like the characters then this is one of the few that is not a buffet.
*Whispering Canyon Cafe- Fun, loud environment. Ask for ketchup.
*50's Prime Time Cafe - Servers are "family". You may get scolded by your "Aunt" fro putting your elbows on the table or not eating your veggies but it's all in fun.
*Coral Reef - Alot more quiet then the others but the kids can watch all of the fish in the giant aquarium while eating
There aren't really any non-kid friendly restaurants in Disney except Victoria & Alberts and maybe some of the signature restaurants.