I just emailed a list of Korean restaurants to my cousin at his request and thought that some of you might also be interested.
Here are the places that come to mind. Of course, there are a 1000 other Korean places, but most of the ones below are the places my family goes to pretty often. It seems like there's a cycle of restaurants. Every so often, it changes. Here's what's in the current rotation for us.
On the southeastern corner of Western and First, across from HK Market
My family likes to get the "got sal" type of beef. I forget what it's called in English. They have the rice wrapper thing. The naeng myung (the noodles in cold broth) is good too. I think that if you want a private room, you have to reserve it.
Shik Do Rak
2501 W Olympic Blvd (east of Vermont, on the north side of the street)
Pretty popular with young people. It's fairly cheap. The quality of beef isn't the greatest, but it's not bad. They have the rice wrapper thing. Their combo options aren't bad. There can be a wait.
Sa Rit Gol
3189 W Olympic Blvd (on the north side of the street in a mini-mall)
My family likes the "sam gyup sal" here. That's the stuff that looks like thick bacon.
On Olympic, west of Western, on the north side of the street
All you can eat for something like $15. I haven't been there in a very long time, but I've heard it's very popular, especially among young people. You can also smoke because it's a covered patio.
3330 W. Olympic Blvd. (just west of Western on the south side of the street)
This is the nicest place in Koreatown, ambience-wise. It's where people take non-Koreans and if they're taking guests out. The outside area is the best. I don't think the food is worth the prices, but it's definitely a nicer environment than at other places.
3986 Wilshire Blvd. (at Wilton on the south side of the street)
I haven't been here in a while, but it's one of the nicer places in Koreatown. I've heard it's fairly expensive, probably somewhere along the lines of Chosun Galbee.
Soot Bull Jeep
3136 W Eighth St (on the south side of the street)
We went there years ago and were not impressed. It was written up in the LA Times, so it has quite a non-Korean following. You cook with charcoal, rather than electric, so some say it tastes better. It's definitely smokier.
3450 6th St (at Kenmore in a mini-mall on the south side of the street)
We used to go there a lot in the past, but we haven't been there in a long time. I'm not sure why that is. It's a small, neighborhood kind of place.
Baek Hwa Jung (not sure how they spell it or if they even have an English sign)
On the northeastern corner of Olympic and Norton.
Amazing pork BBQ and other pork items, or so they say. I don't eat pork, but my family loves it here.
Dong Il Jang
3455 W 8th St (on the north side of the street)
This place is great for the thinly sliced round "ros gui." That's what Koreans call it. And afterwards, they make fried rice for you. It definitely has a hole in the wall feeling to it.
1833 W. Olympic Blvd. (east of Vermont on the north side of the street)
This place has the best Korean shabu shabu. They call it Genghis Khan. I love all of the vegetables that come with it. They also make rice gruel for you afterwards which is great.
Soondubu (Tofu soup):
BCD Tofu House
3575 Wilshire Blvd (east of Western, on the north side of the street)
It's 24 hours, and it's a big place. It's always crowded, and they have good combos with kalbi and bulgogi. By the way, all soondubu places use MSG, so be careful if you're allergic.
So Kong Dong (just west of Vermont on the south side of the street in a mini-mall)
2716 W Olympic Blvd Ste 104
I haven't been here in a while, but I remember not liking it because the soup was too beefy for me. But others disagree.
Beverly Soon Tofu
2717 W Olympic Blvd Ste 108 (just west of Vermont on the north side of the street in a mini-mall)
I don't remember if I've been to this one. BCD is just too convenient for us.
Hand cut noodles (kalgooksu):
4008 W Olympic Blvd (just west of Norton on the south side of the street)
It's good for a quick meal. They have noodles, dumplings, etc.
BCD Tofu House
1001 S Vermont Ave Ste 102 (at Olympic in the mini-mall on the southwestern corner)
Everything's ok here. Not the best, but it's 24 hour and good for a quick meal. The one next door Nakwon is also 24 hour but never has as many people in it. This place is very popular with non-Korean Asians.
Western (in a mini-mall across from Koreatown Plaza, south of Olympic next to another BCD)
Everything's good here. I really like their bibimbap (the non dol sot kind). It's called San Che Bi Bim Bop. It's the cold version, but they give you so much. Their kalgooksu (hand cut noodles) are also good. Their spicy noodles are good too if you like kimchi and spiciness.
950 S Vermont Ave (north of Olympic)
It's a "fancy" Korean place. I don't like the ambience. It's pretty old. They need a renovation. They serve the food by courses. My family's not a huge fan. It looks impressive because there are so many dishes, but in the end, we feel that the food isn't that great.
Chung Ki Wa
3545 W Olympic Blvd
Good galbi/naeng myung combo for lunch. They bring it to you cooked for lunch.
2740 W. Olympic Blvd. (just west of Vermont, on the south side of the street)
It has the best vegetables and fruits in terms of quality and price. For example, I bought a big bunch of fresh spinach for 50 cents and every piece was good. Also great scallions, so much better than the kind at American markets. They also have a good prepared foods section in the back to the left. If we have a busy week, we'll just buy some stuff and have it on hand. We also always buy dumplings from the freezer section to have on hand in case we're busy. We get the ones in the orange and green packaging. The brand is O'Hana or something like that. We like the "kimchi and beef" ones. They also have kalbi and bulgogi marinated for you. We also like to get kimbap there. It's close to the front of the store on the left side. We get the ones from Seoul House or something like that. They use the best quality beef. There are also two or three places where you can eat in the market. The kimbap place in the front on the right is famous for their Blue House kimbap. The Korean president years ago tried it and liked it, hence the name Blue House (which is Korea's equivalent of our White House).
Anyway, if you have any questions, let me know. Hope that helps. I'll let you know if I think of anything else.