Some of the resorts have scheduled character dining, you'll have to check with the resorts closer to your trip. Most of those are Scooby Doo and gang, and I think they have a few with the Simpsons.
There is also a character breakfast at Confisco Grille every day at the front of Islands of Adventure. It's a breakfast buffet with great muffins, cereal, eggs, grits, pancakes, cinnamon French toast, fruit, bacon and sausage, and a few other things. They have the BEST Spiderman ever there, plus the Cat in the Hat and Thing 1 and Thing 2. Spiderman knows everything about "himself" from both the comic books and the movies, and his mannerisms are perfect. He even has the voice from the cartoon they had a long time ago. The Seuss characters when we've been there the past two years have been very funny and know how to interact differently with different age kids and adults.
Which reminds me, I need to get going on my TR....
As for other meals, there's really wide variety of food and environment available. Take a look at the website and get a few ideas of what you might be interested in. Most of them have a kid's menu, and everyone here can answer any more specific questions. You might also want to look at the food pictures here.
http://www.disboards.com/showthread.php?t=1031541
For your really nice meal, you may want to consider lunch at Mythos. It has great food, a kid's menu, and a really wonderful atmosphere. Or if you want it at the end of your trip as a last happy memory before you finish packing, The Kitchen at HRH has really wonderful food, too. The hotel restaurants generally have higher prices on food, but the ones we've eaten at have been GREAT. Heck, most of the restaurants on City Walk have great food, and for really reasonable prices, too! And there's something available for every taste and mood.
Hope that helps!