Hi there Alicoo and welcome to Korea and KOTR! If you are living in Jeonju, then you should have pretty easy and good access to lots of climbing areas and a few gyms. Just click the gyms link on the left scroll bar and see what is near you (Albawi and Opera House at Maisan Provincial Park are great areas, as is Seonunsan Park's Seoksal Bawi and Mun Bawi). There are a few KOTRers in Jeonju, and if you contact one of them you might find yourself in the same area and going to the same gym. Try sending a pm (private message on KOTR) to Seungbin, as he's a really cool local with awesome English and a passion for all climbing... If you need to do any gear shopping the climbing shops in Seoul around Jongro-5-ka (종로5가) are cheap and plentiful. Though there are also a few shops in Jeonju itself. Look under the gear shops link and you should find something.
There will be heaps of climbing happening every weekend, all over Korea and beginner or expert I'm sure you'll find both the expat and local climbing communities really open and friendly. Try these KOTR links for some more help too:
Finally, there is a group of folks heading over to Ganhyeon crag this coming weekend (Sept 4-6). It's sport climbing with super convenience, good camping/ min-bakking (kinda like a back-packers thing) and a great atmosphere. Just check out the link:
From Jeonju, you can get a Bus (4 per day starting at 9am, last one at 4pm - takes 3.30hrs and costs 14,500won) from Jeonju Intercity Bus Terminal (전주 시외 버스 터미날) to Wonju city in Kangwon-do (강원도의 원주) and then you'd need to either find a regular city bus (#52 or #53 I think) or taxi it (15,000won abouts) to Ganhyeon Resort (간현 리조트)...OR if you act fast and pm Jerry (KOTR dude in Wonju - JerrBear) he is coming out Fri night and again Sat morning....he might be able to give you a lift or at least help you get on the right bus etc. Another super person! This will be a great weekend with lots of fols from Busan to Seoul, and everywhere else, in attendance. Sport gear only needed as well as camp gear...shops and stuff right there too. I'm eaving from Daejeon, about 1 hr north of you, on Fri morning....but if you wanted, I could probably give you a lift back from Ganhyeon on Sunday.
Hope to see you out there!
Hope that helps you out. Oh, and also do fill in your profile page a bit, as it helps others help you with regards to partners, gear and grades etc.