For a quiet sit-down breakfast, the Grand Floridian Cafe is very nice. It's very quiet during breakfast and the food is very good. They offer several special items including their famous lobster eggs benedict and stuffed
croissant.
I love Kona Cafe for a sit-down breakfast, but it's not always quiet as it's in the open lobby of the Poly Resort. But their breakfast entrees are wonderful. I'm looking forward to their macadamia nut pancakes in two weeks.
For a non-character buffet, I've heard Boma is amazing. I've never been to the AKL, one day I'd love to try Boma.