If you're looking for a breakfast table service meal in a park that doesn't have characters I think you're out of luck unless you want to eat at the Rainforest Cafe at the Animal Kingdom. And technically that's not really in the park ... more like the outer fringes.
There are some great table service places for non-character breakfasts at various resorts: Kona Cafe (Polynesian); Grand Floridian Cafe (Grand Floridan); The Wave (Contemporary); Boma (Animal Kingdom Lodge); The Captain's Grille (Yacht Club); Kouzzina (Boardwalk).
That's all I can think of right now.
EDITED: Sorry ... I included Boma which is a buffet. But as a person who normally doesn't like buffets, I just have to say that they have one of the best breakfast buffets on property. It's terrific!