Hi Michael!
I would give Playhouse Disney's Breakfast at Hollywood and Vine (Hollywood Studios) a shot!
The restaurant sort of has that birthday party atmosphere, as the Playhouse Disney characters (Disney's Little Einsteins and Jo Jo and Goliath-who they're probably less familiar with) are accompanied by a host, who sings and gets all the kids dancing. They'll usually stand in an open area where the kids can walk up and dance with them, sometimes they'll even have them walk in line together around the restaurant, sort of "Conga-line" style...
My daughter did this when she was 4 and loved it!
The food is buffet, with all the breakfast favorites such as sausage, bacon, fruit, etc.
...Also, don't forget to stop by guest services either at your resort or at the park, so your children can get a free Happy Birthday pin! The cast members immediately recognize the pin, and watch them get sprinkled with additional "Happy Birthday's!" as you all walk through the park.
Have a magical time!