I love the previously-mentioned
M. Henry, in Andersonville; it's my second favorite breakfast place in the city. My number one favorite in the city is Bongo Room, which has locations in the South Loop and Wicker Park. Same kind of thing as M. Henry, with egg dishes, pancakes, etc. I had a dish there that was mmmmmmm good - blueberry pancakes topped with almond panna cotta cream. You can find their menus at
menupages. My favorite in the suburbs is
Walker Brothers.
Other breakfast places I've enjoyed include Orange on Harrison (in the South Loop; they have a location on the north side too) for egg dishes, pancake "flights", and customize-your-own fresh juices;
Original Pancake House (same franchise as Walker Brothers, with a similar menu and quality) on Bellevue Place and at Clark and Armitage;
Wishbone;
Flo;
Kitschn; etc.
Keep in mind that most of these places are crowded on weekends, and waiting times to be seated could be lengthy. Since you're talking about a Sunday, you might prefer to do a Sunday brunch somewhere, since such places usually accept reservations. These generally fall into two categories - places that do an excellent a la carte brunch (there are many; ones I've enjoyed within the past year include
Sola in North Center,
Magnolia Cafe in Uptown, and
Cuatro in the South Loop), and places that do a big buffet, like the uber-expensive upscale restaurants in the luxury hotels off Michigan Avenue (
NoMI in the Park Hyatt,
Seasons in the Four Seasons, the
Greenhouse in the Ritz-Carlton).