I already attend this cafe and it's great.
Across from Thursday party near Kyungsung University/Pukyung Universtiy Station. (4th floor of BBQ chicken building)
LZONE Cafe 4F #58-35 Daeyeon-dong, Nam-gu, Busan, Korea.

You can study Korean, English, Spanish, Japanese and Chinese. Plus you can just hang out with many cool people and there is a good party every friday night with all you can drink beer.

Great for Korean people who just want to talk with foreigners or foreigners who want to make Korean friends (or with other foreigners). Also just a great place for anyone who likes to study languages.
Private and free talking classes available.
Find it on Naver (http://cafe.naver.com/lzonecafe), Facebook (search for Lzone) and you can email for more information to help@lzonecafe.com (email Andy, he's one of the owners).
If you live in Busan or are just visiting you can try it out for 10,000원 for one day. Otherwise buy a membership and I'll see you there!