err.. depends on your preference.. i can be only in seoul for 1 week eventhough i been there numerous times. it's just like my hometown 

you can go to mt sorak

been staying in Seoul for 1 year now. Stayed in Yeosu for 3 months as wel (loved this place).
Traveled to Busan, Yeosu, Jeonju, Suncheon, Nami, and next week Donghae and Jeju.

Used to club a lot in Itaewon and Apujeong area. Gangnam was also one of my regular place for cafe and drinking but, after a while, it gets real boring.

My favorite place is Busan so far and also Suncheonman Bay. Prefer those nature nature place. 2 more months to go before I am back to Malaysia for good.

I am furthering my MBA here. Stayed in Yeosu for 3 months due to work attachment there with my current Korean company.
 

I used to withdraw thru Citibank ATMs (widely available), using Maybank debit card, there's a RM10.60 charges, but rates would be better than money changer in KL.
Advisable if you're withdrawing 700k-1mil.
Other than that, bring USD to exchange at Myeongdong also better rates.

going there in 2 weeks
i'm only bringing heat tech shirt and pants, uniqlo ultra light down, some scarf, winter hat, glove and mask to block the wind
the usual