Seoul & Busan by Bullet Train, 5 Nights

From Incheon over the long sea bridge and into the city, a drive of a little over an hour. Check-in is from about two in the afternoon. The first evening is for finding your feet: Insadong's lanes of tea houses, paper and brush shops, and the Ssamziegil courtyard with its ramp of small craft stores. It is a short walk from there to Jogyesa, the city-centre temple of the main Korean Buddhist order, lit with lanterns in the weeks before the Buddha's birthday.

Gyeongbokgung, the Joseon dynasty's great palace, is closed on Tuesdays, when Deoksugung takes its place. The throne hall and the pavilion floating on its lotus pond are the parts to linger over. Bukchon's hanok alleys climb the hill behind, still a residential neighbourhood. The afternoon rides the Namsan cable car to N Seoul Tower for the whole basin of the city ringed by mountains, and a visit to a ginseng centre explains the root Korea is known for, before Myeongdong's shops and street stalls in the evening.

North towards the border with a packed breakfast and your passport. The route passes Imjingak, where the Freedom Bridge carried returning prisoners of war in 1953, then enters the controlled zone for the Third Infiltration Tunnel, dug under the line and discovered in 1978, and Dora Observatory, which looks straight across into the North. Sites can close at the military's discretion, and the tunnel and observatory are shut on Mondays and public holidays, when the day is moved. Back in Seoul by mid-afternoon; the evening is free, perhaps for the night market at Dongdaemun, which runs until very late.

Seoul Station to Busan by KTX, roughly two hours forty, through the farmland and hills of the interior. Luggage racks are at the ends of each carriage, which is why one case per person is sensible. In the afternoon, Gamcheon Culture Village: stacked pastel houses built up a steep slope by refugees during the Korean War, now threaded with murals and small galleries. Down at the harbour, Jagalchi market sells live seafood on the ground floor and cooks it upstairs; BIFF Square and Gukje market are next door.

Haedong Yonggungsa in the morning, while it is quieter: a temple built on the rocks at the water's edge, reached down a stairway past stone lanterns. Then south to Haeundae, Korea's best-known city beach, and the walking path around Dongbaek Island to the Nuri Maru pavilion, built for the 2005 APEC summit. If time allows, the Oryukdo Skywalk is a horseshoe of glass over the cliffs where the East and South seas meet. At night the Gwangan bridge is lit across the bay.

Breakfast, check-out and the KTX back to Seoul, then on to Incheon for the international flight; allow about four and a half hours from Busan hotel to airport check-in, so this suits afternoon and evening departures. Some itineraries route home through Busan's Gimhae airport via another hub instead, which saves the train; we advise on whichever is simpler for your flights. There is time at Seoul Station for a last bowl of noodles.