I went to a palace themed coffee shop in Hongdae, Seoul, Korea called 공주가 사는 궁전같은 카페 (“Where a princess should live”). The coffee shop has individual tables sort of hidden away, mostly meant for couples, but I saw a few groups of females there as well.
My favorite coffee shop in Cheonan, South Korea is Dream in the Sky (하늘그림). It’s such a relaxed atmosphere to study or chat in. It’s perfect for groups up to four people. Around once a month they have a jazz night with live musicians. They’re open 11:00 am - 12:00 am, Monday to Saturday. Between Lotte Mart and Nazarene University in Ssangyong-dong.