Hi Michael,
At the Magic Kingdom, I would suggest Cosmic Ray's Starlight Cafe in Tomorrowland. On the lower level, there is a kid-friendly show by resident alien, Sonny Eclipse. He's a cute audio-animatronic! From the age of 2, my son had loved eating here. The menu is varied and it has a great toppings bar!
Another Magic Kingdom option is Pinocchio's Village Haus. Sit by the indoor window that looks into the It's A Small World Attraction. Wave to the boats as they float by! Or sit outdoors on the second floor balcony for a view of Fantasyland.
At the Animal Kingdom, Flame Tree Barbecue has seating along the water with views of Expedition Everest. This location is outdoors. For indoor dining, head to Restaurantosaurus where the kids' meals are served in a sand bucket. Look at the "artifacts" left by student paleontologists and then when your meal is complete let your 4 year old run off steam at the Boneyard playground.
My son has always loved eating at the Backlot Express at Disney's Hollywood Studios. It's fashioned after a movie prop shop. Lots of fun things to look at and a
good menu. The nearby Pizza Planet has arcade games.
In Epcot, dine outdoors at Electric Umbrella for a view of the dancing water fountain show. Dining in World Showcase offers an assortment of fun including sweeping views of the lagoon from La Cantina de San Angel. American eats can be found at the Liberty Inn where you can dine outside and listen to the Fife and Drum Corps!