the tang soo yook that kagehitokiri is basically sweet and sour. you can get it with chicken, beef, or pork. it is a chinese dish, although many places it's "koreanized." very tasty.
as for traditional korean, powerplantop has the first 2 nailed - kalbi (or galbi) and bulgogi. the best kalbi places will have a grill at your table and will use hot coals rather than gas. it really does make it taste better, imo. note, though, that you WILL leave the restaurant smelling like meat! a couple notes to add re: bulgogi - it is thinly sliced marinated beef and they generally cook it in the kitchen, not at your table.
another accessible dish is bibimbop. kagehitokiri mentioned "yook hwe bibimbop." the "yook hwe" part indicates the raw beef. you can get regular bibimbop which is the same, but with bulgogi. you can also get dol-sot bibimbop which is in a hot stone bowl (yellows and hardens the rice on the sides) and hwe dup bop, which is basically sashimi bibimbop.
if you don't mind spicy, go for some soon dooboo jji gae (soon dooboo = soft tofu, jji gae = stew). hot (temp) and spicy and can get with beef, seafood (prawns, muscles, clams, etc), mixed (seafood + beef) or plain. there are a few other varieties and you can request varying levels of spiciness, from white to medium to hot to very hot. don't forget to break your egg in the bowl right when it comes out!
a very good summer dish is mool naeng myun (mool = water, nang myun = buckwheat noodles). it's basically buckwheat noodles in cold soup with some sliced beef, cucumbers, a slice of pear, a boiled egg, and maybe a few other veggies. you typically add some hot mustard and/or hot pepper paste and some white vinegar. VERY good and refreshing on a hot day.
as for restaurants i like:
in detroit or ann arbor, seoul garden was always the "nice" korean restaurant when i was a student at U of M. kana in downtown ann arbor (west liberty, was it? been a while) was also pretty good (knew the owners back in the day).
in atlanta, i really like chodang soondooboo (cho dang tofu house) in doraville on buford highway. just south of chodang is a place called haw woon dae kalbi, also on buford. the owner is a friend of my father and the kalbi is excellent. both are outside the perimeter. for korean-style chinese food, i recommend pung-mie or yen-jing, both on buford in doraville, but inside the perimeter. yen-jing has better jja-jiang-myun (noodles with blackbean sauce), imo, but can't go wrong with either. they also have traditional chinese dishes, too, of course.