If you want to get anywhere in Seoul you should use the subway. Korea has one of the best subway systems in the world. I think subway is the best way to move around the city. It is safe, clean, inexpensive, well organized, foreigner friendly and very easy to use. The stations are announced in multiple languages (Korean, Japanese, Chinese and English) so you won't get lost. There is a lot of different lines and stations so it can be a bit overwhelming at first but it's actually pretty easy to figure out and use, especially if you use an app.