When the time comes to see Korea you might want to consider either a motorcycle or a rental car. We've used both for years now. When we road tripped to the DMZ we rented a car. For us it was super easy. You just need a passport and a driver's license. We went the extra mile and got an International Driver's Permit. All we had to do was go to AAA in the USA and show them our driver's license. For 15 dollars they print you our an international license and you're good to go.
To rent a car in Korea it should cost you about 150,000W or $130 for four days. Awesome.
You can even get a propane fueled car and save some extra cash on fuel.
The motorcycle was even classier though.
For 300,000 W or about $300 we got this sweet beauty. $20 a month in fuel and endless miles of pristine Korean highway.
I never felt so alive.