You have so many options, Sarah! Here are a few that jump out at me, based on the ages of your children (though none of these are character meals):
'Ohana - my kids love the coconut races that take place in the dining room. They're big fans of the pan-Asian (though familiar enough) menu items, too!
Teppan Edo - just today my four-year-old son told me this was his favorite restaurant. If your kids are fans of hibachi style restaurants at home then they'll enjoy this Epcot eatery.
Sci-Fi Dine-In Theater - You eat in parked "cars" while watching movie clips in a dimmed theater. Could there be anything cooler?
Whispering Canyon Cafe - Famous for its all-you-care-to-enjoy canyon skillet, this restaurant offers both hearty meals and dining room antics sure to keep your kids in stitches through the meal. I would tell you all about the fun, but I don't want to spoil the surprise!
These are favorites for my kids; I bet yours will enjoy any of them! Have a great trip.