Hello Meghan!
My top pick for you would be
Chef Mickey's located in the Contemporary resort. Here you can dine for breakfast or dinner and have Mickey, Minnie & friends visit your table.
My second choice would be
'Ohana for breakfast, located at the Polynesian resort. Here you can dine with Lilo & Stitch and friends. The breakfast is served family style at it's delicious!
Another one of my favorite character meals is
Crystal Palace in the Magic Kingdom. Here you'll be able to dine with Winnie the Pooh and friends. When my children were younger, they enjoyed breakfast the best as they serve character shaped waffles.
If you're looking for a fun (and loud!) atmosphere with no characters,
Whispering Canyon Cafe for dinner would be a great choice. However, given the ages of your children, I think they would enjoy one of the character meals above best.
I hope you have a magical vacation! Diane