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.
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.