Seoul

The grandest of Seoul's five royal palaces, the seat of the Joseon dynasty — sweeping tiled roofs, a throne hall reflected in a lotus pond, and the mountains rising behind. Come for the changing-of-the-guard ceremony, and rent a hanbok (traditional dress) nearby to get in free and feel part of the scene. The essential first stop in old Seoul.

A hillside maze of traditional tiled hanok houses between the two main palaces — narrow lanes, curved eaves and sudden views over the old city to Namsan tower. Still a living neighbourhood, so wander quietly; it's the most photogenic corner of Seoul and a window into how the city looked for centuries. Combine it with the tea houses of Insadong below.

The tower crowning Namsan mountain in the centre of the city, and the best view in Seoul — the whole endless metropolis spread below, magical after dark. Ride the cable car or walk up through the park, clip a 'love lock' to the fence, and time it for sunset as the neon comes on. The classic Seoul panorama.

Seoul's great edible ritual — marbled pork belly or beef grilled at your own table, wrapped in lettuce with garlic, kimchi and ssamjang, washed down with soju. Noisy, smoky and communal, it's the meal you'll remember; find a busy back-street joint where the locals eat, and let the staff show you how it's done.

The most beautiful of the palaces and a UNESCO site — pavilions that follow the contours of the land rather than a grid, and behind them the exquisite Huwon 'Secret Garden' of lotus ponds and wooded pavilions, entered by guided tour only. Quieter and more graceful than Gyeongbokgung; book the garden tour ahead, especially in autumn.

The city's most famous old market and a street-food paradise — sizzling mung-bean pancakes (bindaetteok), knife-cut noodles, gimbap rolls and the raw beef tartare that made it a TV star, all eaten elbow-to-elbow at packed stalls. Cheap, chaotic and delicious; come hungry, point at what looks good, and squeeze onto a stool.

Seoul's neon shopping mecca — a grid of streets crammed with K-beauty stores, fashion, and after dark a carnival of street-food carts selling cheese-pulled tteokbokki, egg bread and tornado potatoes. Frantic and touristy, but a fun, only-in-Seoul evening; graze your way through the carts and watch the city shop till late.

The university district that is the engine of Seoul's youth culture — buskers on every corner, indie live-music clubs, cheap bars, and dance clubs that pound till sunrise. Younger and grittier than Gangnam's glossy scene; start with street food and a hof (beer hall), catch a band, and see where the night takes you. Seoul at its most alive.

A restored stream threading right through downtown — a sunken ribbon of water, stepping stones and greenery below the traffic, where office workers eat lunch and couples stroll at night under the lit bridges. A lovely, unexpected escape in the heart of the city; walk a stretch of it, especially in the evening or during a lantern festival.

Zaha Hadid's swooping silver spaceship of a building, the icon of modern Seoul — a curving landmark of exhibition halls and design shops, spectacular when lit at night and often surrounded by an LED sea of roses. Wander its flowing forms, then dive into the 24-hour fashion markets and street food all around. Old-and-new Seoul in one spot.

The wide river that splits the city is lined with grassy parks where Seoulites cycle, picnic, fly kites and order fried chicken and beer to the riverbank by app. Rent a bike, join a summer evening crowd for the Banpo Bridge rainbow fountain show, or just watch the city unwind. The best free window into everyday Seoul life.

The old cultural street of Seoul — galleries, calligraphy and craft shops, traditional tea houses tucked up staircases, and the Ssamziegil spiral of little studios. Touristy but genuinely charming; sip a cup of citron or ginseng tea, browse for a hanji-paper souvenir, and slow down amid the palaces and hanok lanes around it.

The Korean bathhouse experience — hot and cold pools, steam rooms and kiln saunas, then lounging in shared halls in matching pyjamas with a shaved-ice bingsu and a hard-boiled egg. Cheap, restorative and utterly local (some stay open 24 hours as budget crash-pads); a wonderfully odd, only-in-Korea way to unwind after a day on your feet.

The glossy south-of-the-river district of the K-pop and luxury world — flagship stores, the vast COEX Mall with its Instagram-famous Starfield Library of soaring bookshelves, an aquarium, and the serene Bongeunsa temple sitting incongruously among the towers. A dose of hyper-modern, moneyed Seoul, and a fun contrast to the old palaces.

One of Asia's great museums, and free — a vast, beautifully laid-out collection tracing Korea's history from prehistory to the Joseon court, its treasure a gilt-bronze pensive Buddha and a soaring ten-storey stone pagoda in the central hall. A cool, calm and rewarding half-day that gives real depth to everything else you'll see in the city.