I will stay in Seoul, South Korea for about four months. After that I want to travel the country. Any recommendations about what to see apart from Seoul and Busan? I'd really like to experience the rural areas.
Are you into camping? Muuido and Seonyudo are beautiful islands off the west coast - Muuido is easily accessible on the Seoul metro (plus a short ferry), and Seonyudo is a little further south (about 3 hours by bus to Gunsan, plus an hour ferry to get to the island), and it's perhaps the most beautiful place I have seen in all of South Korea thus far.
Seoraksan is a great climb, if you're into hiking. It's east of Seoul and you can take a bus there as well. Jeju-do, South Korea's "hawaii" and honeymoon destination, is covered in palm trees and lava caves. The fabled "woman divers" are here as well, and to see them is worth the trip to Jeju alone. You can ferry there from the southern tip of the peninsula, but we found it more practical and economical (and much less time-consuming!) to take a flight there from Seoul - it takes about an hour and prices are around USD $75 round trip, check out jejuair.com for details.
Also beautiful is Haeundae beach, just outside of Busan on the Southeastern tip of the peninsula. Busan is a great destination on its own, but Haeundae beach is famous throughout Korea.
Lots of places to see! There's also a lot of outdoor activities to do around the country and even within Seoul itself, if you find yourself here for a while - like wakeboarding, and hiking, and seeing the temples and market streets... not to mention the amazing norebong rooms (karaoke!), and jimjilbangs (Korean spas, cheap, luxurious, and open 24hours!).
Check out my blog if you like, there's some more info there on our favourite things to do here, pictures from our adventures, and more detailed directions on how to get to different places... Good luck! It's a great country! :)
Seonyudo: (http://vagablonding.wordpress.com/2010/06/09/vlog-beach-camping-on-seonyudo/) about 7 years ago
http://hiddengemtravel.blogspot.com/search/label/South%20Korea ( here's some info on Seoul and other parts of Korea) over 5 years ago
I'm quite partial to Gwangju (in the south) and its surrounds. There are some beautiful temples (particularly Daewonsa) near Gwangju and some great hiking (Wulchasan specifically).
Mokpo is a cool little port town from which you can explore the many islands off the west coast. Bigeumdo and Oaedaldo are my favorites. Wando to the south is nice too.
Jeju is an obvious suggestion, and I really loved my visit to Jinhae for their Cherry Blossom Festival. about 5 years ago