First of all, make reservations at any sit down restaurant you are going to eat at and make them now! Some of the better restaurants are probably already booked since many people make them exactly 180 days from when they are going.
As for places, Chef Mickey's (at the Contemporary) is pretty good and the characters are fun. The Crystal Palace at the Magic Kingdom is another fun one. Ohana at the Polynesian is really good food and a fun atmosphere, but if your kids aren't willing to eat Asian inspired food, probably not a good choice. We also love the character breakfast at the Grand Floridian. Great food and fun characters (Alice in Wonderland, Pooh, Mary Poppins, etc.)
Epcot has a dinner with the princesses at the Norwegian restaurant. I don't know how good it is (this is our first year trying it), but it sounds delicious! If your family is willing to eat and try new things than any of the countries in Epcot are FABULOUS!!! Our personal favorites are Canada, France, Japan, Mexico and Morocco. The Coral Reef Restaurant has a pretty cool atmosphere, but we have been disappointed with the food the past few times we have gone.
Hollywood Studios has a really fun restaurant for kids called the Sci-Fi. You eat in old "convertibles" while at a "drive-in movie". The food is pretty good, but the atmosphere is what makes it so much fun. Your kids would love it!
We also really love the Cape May Cafe at the Beach Club, and have heard that Cat Cora's restaurant Kouzzina at the Boardwalk is pretty good too. Hope this helps and have fun! :)
P.S. After looking at other responses, I agree completely with the T-Rex one too! My son thought that place was SO cool, and the food was really quite good considering you really go for the atmosphere!