Good Korean for vegetarians & meateaters?
Chosun Galbee - high end, great food, good for dates, or business people
Soot Bull Jeep - good food, but grills are charcoal flamed, you'll walk out smelling like a smokehouse
Sa Rit Gol - unique panchan, casual
You may want to try Japanese BBQ instead. Most non-koreans find this style and cuisine more appealing. Gyu-Kaku is a great place for Japanese BBQ.
Check the internet for locations.
I would seriously reconsider taking a vegetarian to a Korean restaurant, particularly one w/ charcoal grills. For sensitive vegetarians, it could be very difficult to spend the entire meal watching meat being cooked in front of them at the table & be completely surrounded by the smell, etc. It would be a much better idea I think to go to a Japanese restaurant or something else in the nearby area where everyone can order what they like, but you won't have to worry about vegetarians feeling assaulted by the meat.
I just had this challenge and we went to Kobawoo House on he corner of 7th and Vermont. It totally fit the bill. The specialities of the house are the meng bean pncakes (the kim chee one is vegetarian but if your friends eat seafood, the seafood pancake is spectacular). They also have this cold acorn noodle dish with vegetables that is also vegetarian and fantastic. For the meat eaters, the cold, sliced braised pork is also a winner. All of these dishes are featured on the menu as house specialties. This is not a BBQ place, so no cooked meat smell.
I'd recommend avoiding a Korean place if there are vegetarians in your party. In general, Koreans eat vegetarian fare at home-- they'd rather spend money on meat (and the grills required for it) and fish when they're out. You're very likely to run into little bits of seafood and meat even in seemingly "vegetarian" things like kimchee. Most types of kimchee contain jut-- little shrimp? krill? something of the sort. The only completely vegetarian things I can think of are rice, tofu, and dotori-mook (acorn jelly), but you don't want your friends eating that all night.
You could try asking whether a soondooboo (fresh tofu stew) place like BCD could prepare dishes in a completely vegetarian manner.
If you're truly set on Korean, try a place like Dan Sung Sa (on 6th near Berendo?), which does a variety of pub/bar food.
Most cafes also offer salads and simple pastas, but those are more like Koreanized Western dishes.
Sallim was unfortunately taken over by a tofu house. However, there are still a few good places for veggies - I'm a fairly strict vegetarian and was extremely happy with the food at Beverly Soon Tofu on Olympic and Vermont. The bibimbop was delicious and there was plenty of 100% veggie food. I brought my meateating boyfriend there and he was really pleased with his Shrimp Soon Tofu and a beef dish he got...I would definitely recommend.