For specifics on traveling to/from different locations around South Korea click here
One of the biggest problems i encountered getting around downtown Seoul was trying to communicate to taxis where you wanted to go. Even if you had Apple or Google maps pulled up they reacted as if they didn't know how to use a smartphone. The problem is not only are they unfamiliar with these apps, but they display mostly English wherever possible. Download the Daum Maps App. Wherever you see a Daum link in this site it will open in the native app. The roads and places in the app will be listed in Korean so the driver will have an easier time understanding where you want to go.