Soul Factory is a 24-hour practice space located in Seodaemun-gu near Hongik Univ. Station. It's not for whole bands, but for individuals looking to practice alone in fairly small rooms. They say that their rooms can accommodate vocals, guitar, bass, wind and string instruments, and more, but no drums. You can pay by the hour or enter into a monthly contract.
Their website is club.cyworld.com/SOULFACTORY, and you can contact them at 010-4596-4121.
They're located at 서울 서대문구 연희동 421-33 지하1층 (Seoul, Seodaemun-gu, Yeonhui-dong 421-33, B1):