Sorry, no restaurants, but here are the foods I usually eat. (Please excuse the spelling):
Those dumplings are called man-doo. They are usually served steamed or in a broth - both delicious if made right (and they usually are.) Two types (that I know of): goo-gi man-doo, which is made primarily from minced pork with green onion, maybe a little kimchi in it; and kimchi man-doo, made primarily of kimchi and can be spicy. They are served with soy sauce and vinegar for dipping.
Bulgogi - very thin slices of beef served in a broth. The beef is marinated in a very slightly sweet/sour sauce.
Galbi (or kalbi) stew - beef served in a stew.
Mul nang myung - cold noodle soup. Buckwheat noodles served in a broth so cold it's usually slushy along with sliced veggies, a small piece of beef, half a boiled egg and a few shreds of Asian pear for a little bit of sweet crunchiness.
I don't like hot spicy stuff, so my Korean colleagues know to have the restaurant folks tone it down a lot for me. But I once had a spicy pork stew that I have to admit was delicious. But the hot spices became too much that, at the end of the meal, when they serve the rice, you are supposed to put it into the stew bowl and scrape up the remaining stew bits, but my mouth was in such pain that I couldn't even eat the rice, it hurt so bad. Another (western) colleague refers to the dish as Korean risotto.
In general, Korean restaurants specialize in one type of food product, such as beef or pork dishes, but not both and the menu choices are limited. There are no multi-page menus as in some Chinese restaurants. So decide what type of meal you want and ask the concierge for a recommendation for a good Korean meal of (insert desired type of meal here.) I'm sure he will be more than happy to oblige.
Also, Vietnamese noodle shops are quite popular and very good also.