I stayed at the Grand Californian when I was there last, and we had a GREAT dinner at Napa Rose in the hotel. The downside, it's quite up there on the expense list, and you need proper attire for it. If those aren't detractors for you, then I'd suggest making reservations there, they are kid-friendly in the way that when I was there, there was a party with many kids in it that seemed to be having a great time. The other place that I know of in the hotel there is the Storytellers Restaurant, in the mornings they have Chip & Dale in there, and I saw some other characters in there throughout the day as well. So you might have luck with there, it's a bit on the casual side, since it's right by the pool, but the atmosphere is great there.
As far as out in the open, I had dinner at Brennen's (sp) in DTD, and the food was excellent, I love Cajun/Creole cooking, and they know how to do it right. I also ate in California Adventure too, at the Wine Country Trattoria (sp again). It's very family friendly, and the best part, you can get wine there! LOL. THe food was great, but I really reccomend Priority Seating for ANY place you want to eat in the Parks.
My all time favorite eatery IN the parks though, hands down, goes to BLUE BAYOU in New Orleans Square. YOU'RE RIGHT IN THE MIDDLE OF THE PIRATES ride! The food is great, the atmosphere is phenomenal, and it's entertaining because the people going by in the boats can look at you and if you're celebrating your birthday, and they're singing happy birthday to you, sometimes the people in the boat join in. Well worth it!
Sorry if I'm longwinded. And I hope this helps.