For breakfast, there are lots of good places. Two spring to mind immediately: Ina's on Randolph and the Bongo Room (original spot in Wicker Park and satellite location on Roosevelt and State). Both have outstanding breakfast menus. Bongo Room doesn't take reservations, though, and can lead to a longish wait on the weekends.
I'm not sure about Asian but for good breakfast... Wishbone on Lincoln and School, get the Red Eggs, and the Bongo Room in Bucktown... Oh man. They have these waffles drizzled with warm vanilla bean cream... Get a half order. They're SO rich.
If you are from springfield area (or not and want to find out what all the buzz is about) you can get an OUTSTANDING Horseshoe (I recommend the pulled pork)at 6 degrees on Damen in bucktown!!
Other highly notable treat:
The three little pigs at silver palm (not far from 6 degrees) -I dare you to try and finish it!!!
I heard Anthony Bourdain LOVES that sammich-I agree!!
In the Blackstone Hotel on south Michigan, there is a restaurant called the Mercat A La Planxa. They are a tapas restaurant and they were amazingly good. If you sign up for their newsletter, they send you emails with specials going on almost every month. Great idea, and a little-known spot if you are in the "woo-ing" mode. lol.
+1 for the Bongo Room for breakfast in Wicker Park.
Other notables for lunch / dinner:
Kuma's Corner in Lakeview for the best burgers in town.
Smoq in Avondale for the best BBQ in town.
Revolution Brewing Co. for the best homebrew in town!