Here are some of my favorites (in no particular order):
Moon Garden - 20 Donald Drive in Fairfield (off of Dixie Highway). Moon Garden doesn't look like much on the outside, but if you can get past the rough exterior the food is wonderful. You can't go wrong with the Bulgogi (grilled marinated beef served with rice). Don't bother with the egg roll they'll also give you, though. It's gross.
Riverside Korean - 512 Madison Ave. in Covington, KY - I've had their Dolsot Bibim Bab (mixed vegetables with your choice of meat served in a hot stone bowl. They crack an egg on top and the heat of the bowl cooks the egg as you mix everything together). Riverside was on Cincinnati Magazine's Top 10 Restaurants list this year. It's worth checking out.
Sung Korean Bistro - 700 Elm St. Downtown - Here I had the Kimchi Soup. Usually Kimchi (pickled cabbage) is eaten as an appetizer, so this was a little different take on the dish. Tasty.
Kim's Korean - 10548 Harrison Ave. in Harrison - I would also recommend the Bulgogi here. Kim's also does pork cooked with Kimchi for another delicious variation on one of Korea's most famous dishes.
Also be sure to sample the assortment of side dishes/appetizers (Bahn Chan) that will be offered before your meal at most of these restaurants.
I hope this helps. Be sure to report back and let us know how you liked your first experience with Korean.