i dropped into the global village center in itaewon yesterday. it's next to the international clinic.
i was greeted with a super friendly hello, like the girl got up out of her chair and smiled big and cheered, "hello!" from across the room. :)
they had free internet access and some english books (fiction & non fiction) to loan, also for free.
they offer a lot of services for foreigners: help get a cell phone, help get an international drivers license, how to prepare your resume, translation services, how to separate your trash (you can get fined if you dont follow regulations), how to get a credit card, how to do your taxes, etc. I think any question a foreigner has, you can ask them.
i think these centers are all relatively new; most articles ive seen about them were written within the last couple of months. there are several locations, i know of one in yeonnam, one in yeoksam, one in seocho, one in inchon, one in itaewon, i think this here is their main website... at least, the logo looks the same. actually try this link, it's the sitemap and i think it's easier to navigate.