If you're interested in casual dining, try Soliphana off of Golf Rd. in Schaumburg. It's in a strip mall, and unfortunately I can't remember the cross street, although it's past the Melting Pot and Bahama Breeze on the south side of Golf. The decor is very eighties, but it's clean and the food is a good introduction to the basics of Korean cuisine.
Newbies to Korean food usually like the Korean barbecue (bulgogi or galbi) which is grilled meats with assorted condiments, toppings, and rice. You wrap up the meat in a lettuce leaf, and dab in a bit of daengjang paste. Other suggestions are the dolsot bibimbop (rice mixed with vegetables, hot bean paste and meat in a stone bowl - be sure to let it sit a moment before stirring to let the rice get a lovely crispy texture on the bottom for some nice crunch).
I love the appetizer pajun, or haemul pajun, basically a flat pancake with scallions (with or without seafood) that you dip into soy sauce. If you prefer milder flavors, you might like the mandoo guk or duk mandoo guk, which is dumpling soup with or without rice cakes. For spicy flavors, try any of the chigaes, like sun dooboo chige (spicy tofu stew) or yuk gae jang (spicy beef soup).
There's also a Korean barbecue around that same area, as well as a Korean grocery store, all stemming off of Golf Rd. heading west. Yu Mandarin has terrific Korean-Chinese food as well. I'd start off with either the chajangmyun (black-bean noodles), ch'ampong (spicy seafood noodles) or t'ang su yuk (honey-sauced battered and fried pork).
How far northwest are you talking? There are a whole bunch of Korean restaurants along Dempster west of the Edens. I travel this route with some frequency, and think of stopping along the way for lunch. I've been to two places so far, but can't remember the names... These are storefronts, the food I've had so far was pretty decent, but probably not as good as Lawrence avenue in the city.
I'd be interested in hearing more if you try out any restaurants in the near and mid-NW range.
Woo Lae Oak, 3201 Algonquin Road, in Rolling Meadows, is a good place (it used to be in Chicago, in the River North area, then moved to the 'burbs). I don't actually know where Rolling Meadows is - hope it's in the right area for you. When it was here in town, it was a rather more elegant restaurant than most Korean places, and the food was quite good - hopefully it hasn't changed.