My closest friends are mostly other foreigners also teaching at the public schools in my town. There's a lot to bond over in that experience and we've all more or less hit it off really easily. We also have some Korean friends we enjoy hanging out with and they're very nice, but it's a different type of friendship that takes more effort, in my experience. To be honest, after a week of working with my all-Korean staff at school I'm more than ready for some 'waygook time,' where everyone's sense of humor and cultural references and life experiences are on somewhat similar pages. I enjoy my Korean friends but feel more relaxed and able to "be myself" around my foreign ones. Also, one of the best parts about Korea is that while it's easy to bond with other English teachers, we're all from very different places ourselves, and it's awesome that I now have friends from South Africa and the UK and Canada and New Zealand, and have been able to learn a lot about those places.
But having said that, Koreans usually make wonderful friends--they tend to be generous to a fault, kind, considerate and attentive, and very keen on the whole "cultural exchange" factor in the friendship.