I can almost hear some of you protesting that you want to truly experience Korea by making friends and hanging out with only Koreans. I said that too, when I first came here. In fact, I did not even talk to a foreigner until I'd been ehre for an entire year. This was possible because I am the only foreigner in my school.
My excuses were many and maybe I was just waiting for the right kind of person. So many foreigners here delight in Korea bashing, and who wants to hang out with losers like that? In any case, I would advise having at least one foreign friend you can trust and talk to about anything. A Korean cannot understand what you are going through trying to adapt to life in Korea. Only another foreigner can. Visit my best Ulsan friend's website at what I like to call, "Barbara's World."
I think during the first fifty outings with a group of Korean friends, you don't really mind that 90% of the conversation takes place in the form of rapid Korean and no one translates for you. But after that, it can get tiring to watch everyone laughing and having a great time while you stare at your fingernails. Take a foreign friend you can chat quietly with and you'll feel more sociable.
Traveling, shopping, or just hanging out--it really helps to have at least one foreign friend with you sometimes who can understand your Western cultural allusions, TV show quotes, and who is amazed, surprised, and shocked by the same differences between America/Canada and Korea.
It's also nice to be able to just call someone up and chat without figuring out time differences or worrying about phone bills.
You CAN learn about "true Korea" even if you hang out with foreigners sometimes. Most of all, you can all pool together knowledge and experience and learn even more. Totally assimilation is not necessary.
Just take it from one who's been there, done that.