backpack south korea 2 weeks or 1 month??

Well I think two weeksis enough if you don't include Jeju.

If you include Jeju, there is a HUGE tracking course there. So you might want to enjoy bit of those. I belive this tracking course is not included in Lonely planet yet.
http://www.jejuolle.org:8080/eng/
It's not costly to look around Jeju if you follow this tracking course. There are hostels for 10000K. (about US$9) around this traking course. Scenes are great.

If you want to get used to enviroments in Korea, I recommand you to make Korean friends while in Korea. Homestay is one good way, and you can search for list of Korean people who are intereted in becoming friends with foreign people.

I live in Korea, & still haven't seen everything, so if you have the time definitely a month, with some highlights being:

Ulleungdo
Jejudo
Baengnyeongdo
Seoraksan
Busan (3 days)
Seoul (2-3 days)
Boseong Tea
Maisan / Tapsa
Jikjisa
Haeinsa
Beopjusa / Songnisan
Danyang
Hongdo
Gyeongju

Some shots I've taken:

http://www.treklens.com/members/chrisJ/photos/Asia/South_Korea/

http://beta.trekearth.com/members/ChrisJ/photos/Asia/South_Korea/

Nothing much to see in Daegu, so I'd skip that town & just visit Haeinsa.

To cut transport costs to & from Jeju Island, get the KTX train to Mukpo on the south west coast of Korea, & catch the fast boat to Jeju city, which runs twice daily about 8:30 am & 2 pm. Takes 3 hours each way. Public busses go everywhere in south Korea & there are usually a string of Motels near the bus stations for 30-40k SK won.

wow.. thx for the link... jeju seems quite a good place for trekking and relax... i will definately consider including on or two of the trekking routes if i decided to include jeju.. thx

homestay,hmm.. i will try to consider that thx... it will be my first time backpacking and i'm going alone.. not sure if i'd be daring enuf to make friends with the locals.. i'm scared it'd be awkward and have nothing to talk about with them :D

wow chrisj,those are amazing shots u took man.. i'm enjoying my time seeing them... they are beautiful.. thx for sharing..

thx for the suggestions of the places,never heard many of them b4.. i will research and put them into considerations.. ur photos will definately help me a lot....

looks like if i'm going to jeju,i wont be taking airplane from seoul... ur way is definately better,i can explore places on the way to mukpo and take boat to jeju... maybe i will take ferry back to busan from jeju later... thx for the suggestion man.. i initially plan to take ferry/plane from seoul to jeju but i will scrap tat idea...

definately learn a lot tips today.... i will make a much better plan now..

It's 13 hours by boat from Jejudo to Busan. Better to go back to Mukpo, & get a bus to Boseong tea, overnight there, & continue on by bus to Busan, the next day.

And Seogwipo on the south coast of Jeju Island has a lot more to see than Jeju city on the north coast. 3 waterfalls & even a museum above one of the waterfalls, with copies of the terracotta warriors from Xian in China.

I think you should visit Daegu, I had a brilliant time the first time I went there in 2008, and personally I'd give Jeju a miss, though if you do go, please don't stay longer than 3 days as you will get extremely bored. Also visit Gwangju. Would definetely visit other places recommended by "ChrisJ" (Nice photos by the way.)

Not quite sure why you want to stay in Incheon though?, I would visit there from Seoul...

I must warn you, Korea is very ADDICTIVE, I only planned on going there once in July 2008 for a once in a life time trip there, but I've been back there 5 times.. In fact have just got back 2 days ago, (Met a young lady the first time I went, And she'll be staying at my home in Wales until October, then I go back out there with her ^^..)

Another thing I'll recommend, is if you have time, sign up to penpal websites, and try and meet Koreans on there to arrange to meet you so they can show you around their local areas, and most often or not they will always pay for lunch/dinner as they are polite creatures out there ^^, And to return the favour, buy them some drinks in a local bar or something ^^.

Good luck with your trip.

http://www.lonelyplanet.com/south-korea/gyeongsangbuk-do/daegu

Sorry, but I lived near Daegu for a year, & didn't find much to see there. Nightclubs yes, but I'm more into scenery. Jeju is for scenery, not nightclubs, restaurants & bars. Try the Galbijum website for more info on Daegu bars, restauraunts & clubs.

http://wiki.galbijim.com/Daegu

I'm also indonesian and have plan to visit korea on budget trip next year. Please share your experience trip when you back. thanks in advance.