Boatwrights at POR serves a nice breakfast.
I'm assuming you don't want to use a day's admission to go to breakfast inside a park. If that is the case, I think I'd visit a monorail resort. Chef Mickey's begins breakfast at 7am, Kona Cafe at 7:30. I imagine the Grand Floridian Cafe and Concourse Steakhouse start around 7:30 as well. Park Faire at the GF probably starts early as well. When you call to make a PS, you'll know for sure. Anyway for any of these you can take a bus to the MK and then the resort monorail ( boat to GF, Polynesian) to the resorts. I'd allow 2.5 hours but that should give you plenty of cushion. Then return to the MK and take a bus back.
You could also take the bus to AK and eat at Rainforest Cafe. No admission to the park needed to dine there.