My only exception is to have breakfast in Disney's Animal Kingdom as early as possible, so that we're able to see the animals when they are at their most active before the heat hits.
Point is, quicker is better in my book! Breakfast eats up precious park time (or precious sleep time, if you get up early enough to eat before the parks open!).
But don't forget those character breakfasts - they're always fun as well!
We generally hit the parks when they open, eat a Kashi bar while riding the TRAM or waiting for the park opening ceremony, tour until about 11, eat an early lunch, hit some high capacity attractions, then bolt back to the resort until dinner time.
One place in the parks that I actually really like for breakfast is the Sunshine Food Fair in the Land. Get some freshly made breakfast sandwiches on crossants. Very nice!
As for what to eat for breakfast? Pretty typical breakfast. Eggs, bacon and toast. The eggs are great for giving you the energy you need to stay moving 'til lunch. ;)
When under this plan, it's best to use just a snack for just a quick grab and go breakfast, as a full counter service meal plus your table service meal later on in the day is PLENTY of food for an average or ABOVE average adult.
Disneyland trips I would suggest choosing trusted breakfast places (Denny's, IHOP, or Carrow's)...but if you have a rental car, I would suggest skipping those restaurants that literally border the Disneyland grounds...not only are these ones extremely busy because of the massive number of motels and hotels that share they same streets but the prices are often a bit more inflated due to the proximity to the Disneyland resort (just like Niagara Falls Ontario...add at least $2 per entree more than the same menu at the same franchise a couple of miles down the road)
There are several great places to eat breakfast at the parks including Chef Mickey's at the Contemporary, Boma at AK, the Crystal Palace at MK, HRH and one cannot forget the Sunday Gospel Brunch at HOB! If we are just going out for breakfast we will usually hit one of these.