Seoul
Seoul's subway map looks frightening and rides like a dream: every station is numbered, announcements come in English, and a T-money card covers the subway and buses citywide. From Incheon, the AREX express train runs nonstop to Seoul Station in about 43 minutes from Terminal 1, and a little longer from Terminal 2.
The network keeps going well past the city line, which is what makes Seoul a no-car city rather than just a well-served downtown. The subway takes hikers to the foot of Bukhansan's granite peaks and carries day-trippers south to the walls of Suwon's Hwaseong Fortress, and the KTX from Seoul Station makes even Busan a feasible long day out.
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