If it specifically has to be breakfast, the only other one I know of where she appears is Ravello, offered only two days a week. This is one of the more expensive character breakfasts and while I really liked the french toast, I thought the rest of the food was just OK, and if I had it to do over, I'd skip it. It's also a little awkward to get there as the resort is not Disney-owned.
However, if meeting Minnie at a character dinner would be OK, then options would include Mickey's Backyard Barbecue, and Minnie's seasonal dining at Hollywood and Vine -- the costumes are different for each season. I'd choose either Cape May Cafe for a laid back experience, or one of the evening options for a livelier time.
