One of your best bets is to roll west on Chicago and hit up Flo, Green Zebra (Sundays only), or Mexique.. Flo is awesome, especially if you like more savory fare, although their traditional stuff is great too.
There's also the Breakfast Club a block south of Grand if you take the #65 bus west. You could also head east to the West Egg, and believe it or not Fox & Obel has some pretty great stuff in their cafe area.
Check out Orange on Harrison near Dearborn. It spacious and only a brunch joint. Their orange coffee is awesome and they have a more culinary take on breakfasty brunchy items. They have fresh juices you can combine yourself.