Song Do is a hole-in-the-wall Korean BBQ joint in Lincoln Square that is great...don't let the decor fool you.  You might also try a chicken place called Crisp in Lakeview.  I highly recommend both places.

At O'Hare, you will be relatively near a street called Touhy (about 2 miles north of remote parking lot) but then you will have to come several miles east on Touhy.  Then I would make the following boundaries
Touhy to the North
Lawrence on the South
Cicero on the West
Damen on the East

Within those boundaries is the area Lincoln Square that Bigdog mentioned and there are several Korean Restaraunts.  Just north of the Lincoln Square are on Peterson are several Korean Restaraunts. Wish I could hang with ya and have some Bee Bim Bop or Dak bul Gogi(sp)

From what I hear Korean town in Chicago has moved into Niles area.  I've been looking for some good Korean food also.. There's Cho Sun Oak on Lincoln ave & Warner but that's Chicago city area called Lincoln Square. By far the best Korean food in Chicago lol