I skip breakfast in DL or on the drive. I live an hour away and my favorite breakfast spot is at home. A large bowl of cherrios, some OJ and some fruit and I am on my way. I pack an apple and a bottle of water and usually have both shortly after I get in DL. My favorite early morning snack spot, to munch on the apple, is walking down Main Street looking in the windows. Then I have an early lunch at the French Market, which is always filling. I try to get in there soon after they open, maybe 11 or 11:30, when there are less people. So actually my recommendation is, if you can, have a small, healthy, and quick breakfast in your hotel so that you can be on the go in DL - not sitting and eating - and so that you are hungry before the lunch rush hits inside of during.
When I have had breakfast in DL (many years ago) I really enjoyed the Carnation Cafe on Main Street. If I had more than one day in a row I would do that as well. I hear that the Riverbelle Terrace at the edge of Frontierland and Adventureland is a nice place to eat breakfast outside with a view of the River. I would like to try that sometime, if I could find the time. I have also read that was Walt's favorite breakfast spot. It's a toss up whether I would want to give up the table service at Carnation Cafe for the view but buffertia service at Riverbelle Terrace.