One of the best breakfasts in Chicago can be had at Pauline's.
It's on Ravenswood, right along the Metra tracks of the old Chicago and Northwestern line to Milwaukee (now the Union Pacific cut back to Kenosha.... a worthwhile trip too). In an old double storefront building with al fresco dining out front. The place has a lot of character. You're taken back to a time of a few decades past. Complete with authentic signage from the era (I want my green stamps that one proclaims they offer), the diner obviously hasn't changed much over the years. Red and green colors the walls. Even the toilet room has some charm. The food is reasonably priced, if a little more than what you might pay in other locales, but it is worth every penny. Your food will be offered artistically. And it will taste heavenly.
Pauline's is open from 7 - 3 daily and also offers lunch after 10:30 - 11:00. A trip there is more than just a meal, it's an experience.
After eating, take a walk through the neighborhood and enjoy the architecture. (I happened across an old wood garage which is unique.) Or tour the old large cemetery nearby, Rosehill.