As well as the places Olaf Lover mentioned the New York Sandwich place in the Village also does breakfast items including a set menu (croissants, bread etc with a hot drink and orange juice)
I thought Cafe Mickey stopped the character breakfast - have they started it again?
There is a character breakfast you can book in the park - I think at Plaza Gardens - but it is expensive
In the park you can get breakfast items such as croissants and other pastries at several places on Main Street - Market House Deli, Cable Car Bake shop etc