If your looking for more of a natural place to go, then head to Gyeryong Mountain, on the outskirts of Yuseoung.
Very easy to get to:
from Guam Station catch the 107 Bus, which drops you off right at the base. There are lots of very cool shops (curios etc. FArm boy even found himself a pair of practical shoes~see image below) and restaurants to see.
There are quiet a few trails around the mountain, some very steep (found that out on what was supposed to be a pleasant walk in the trees, and turned out to be a 5 hour trek up the mountain side!). But there is a very cool little temple up at the top for photo's and such. A very worthwhile place to head if the hustle and bustle of the city is getting you down :)