We have done breakfast at the Plaza in on Main street a couple of times, and Goofys for brunch once. We prefer the Plaza. It is currently Minnie and Friends. It is a buffet style meal. The hours vary based on park opening time, and I believe it ends at 11. Its a big different then your typical buffet. Some like it, some don't. There are lines to get in, and there is a person on the other side that dishes up your food, makes fresh omelets, etc, rather then everyone touching the food. Some people feel it slows things down. Personally, I like that someone else has not touched my food or sneezed on it! We have not been since its been MInnie and friends, it was Pooh and Friends the two times we were there.
Goofys is at the
Disneyland hotel. We went at 1, so more lunch then breakfast, but the price and food is the same in the morning as it is at 1. Brunch is goes until 2, I think it starts at 7 or 7:30. They also serve dinner. When we were there was saw Goofy, Donald, Snow white and Aladin. Interaction wasnt great, not sure if it was the time of day or if we were just spoiled by our other experiences. Food is served typical buffet, help yourself, style.
Other options that I havent done, but might are: Lilo and stitch at Paradise pier. I've heard its a lot of fun, and I like the option of ordering off the menu rather then just having the buffet. Money saving, and again, no one (other then the staff) has touched my food. The one thing that keeps me from going there is the distance from the park.
The menu/ buffet options is also offered at Storytellers a the Grand. I've heard great things about the food. Its a good choice for those that more more a low key character experience. Its chip and dale, and some others like Koda from brother bear, Meko, etc. They only have characters at breakfast. I think it goes until about 11, like the others.
The other options is Ariels, but that is princesses, and doesnt sound like you want that.