I'm a Wrigley Field season ticket holder and I was having trouble thinking of places I'd recommend. I just thought of Anna Maria Pastaria and noticed it had been posted.
In addition to breakfast, Ann Sather is also a good place for lunch - very hearty "home cooked" type (no longer open for dinner). If the op is going to a day game, breakfast or lunch would be a good choice. And the cinnamon rolls are a must. If any place in the area is
"old school," Ann Sather is it!
I'm also going to post their actual website, because the yelp site posted above indicates a location that is NOT convenient to Wrigley Field. Either the Belmont or Broadway locations is an easy walk from the ballpark.
http://www.annsather.com/