1 Royal palaces
In 1392, King Yi Taejo overthrew the Koryo (hence, the modern name Korea) dynasty to establish his own Yi dynasty. The capital he founded, Seoul, was built within a cradle of mountains around a series of palaces. Of five extant palaces, the most picturesque is probably Biwon. The adjacent Changgyeong Palace was where Yi's royal descendants lived (the last died in 1990). The garden itself was the royal hunting lodge and grounds. Today, it's a forested oasis in the centre of the city, with pavilions and lotus ponds. Information about the city is available at the Seoul Help Centre for Foreigners in City Hall (http://shc.seoul.go.kr or  731 6800).
2 Insadong and Bukcheon
Known to foreigners, for reasons long obscure, as Mary's Alley, this is the best place in Seoul for antiques, reproduction antiques and gifts. The district has undergone a facelift in recent years, with large, modern art galleries and gift shops springing up along the main street. But a few narrow alleys of traditional houses remain, off the main thoroughfare. Insadong is also a good place to sample traditional Korean food. Bukcheon, the residential district behind and to the north of Insadong, features the capital's last significant cluster of traditional homes - 920 of them. A couple have been converted into guesthouses with old-world ambience (paper and timber rooms set around a lamp-lit courtyard) and fair prices (about one-fifth that of the big hotels). They offer a compelling change for anyone looking for something with character.
3 Sinchon/Hongik University Districts
There's old Seoul and there's new Seoul. The Sinchon area is home to three major universities, but if you're expecting dignified plazas of bookshops and study halls, think again. This is a raucous shopping and entertainment district aimed at fun-seeking youth. Outside Ewha Women's University is a sprawl of women's fashion outlets, and between Sogang and Yonsei universities throbs a neon-lit, nightlife zone. The dozens of narrow alleys contain restaurants, internet game rooms, karaoke saloons and smoky bars. About 2am, dedicated party animals head to the nearby Hongik University area for clubs and live music.
4 Coex Convention Centre
Looming over trendy southern Seoul is the giant glass and steel monolith of the Coex Convention Centre. Above ground, this features two InterContinental hotels and the Oakwood serviced apartments. In the basement of Oakwood is the Gimme 5 bar, where you can see live martial-arts fights. In the bowels of Coex proper is a labyrinthine shopping centre, as well as Seoul's biggest aquarium. A juxtaposition of the 21st and eighth centuries can be found behind Coex at the ancient Buddhist Temple of Bomun Sa. Picturesque wooden buildings and Buddhist statuary that are hidden among the colossal architecture of southern Seoul are also home to a shrine for commandos killed during secret missions into North Korea.
If all things Korean become too much for you, head to the expatriate district of Itaewon. Once known for its racy nightlife, the Won has been gentrified lately. By day, it's a shopping district; after nightfall, dining, drinking and dancing take over. Recommended watering holes include the friendly Three Alleys Pub behind the Hamilton Hotel and the famous Nashville on the main street. All That Jazz is the place for live music, and clubs Limelight and Spy stay open until dawn.
6 Samcheong Dong
The fung shui of Mount Bukak so impressed Yi Taejo's advisers that he erected his main palace, Gyeongbok, at its foot. (It's no coincidence that the presidential Blue House sits directly behind the palace today.) To the right is the district of Samcheong Dong, its tree-lined main road home to small shops, restaurants and wine bars, many set in converted traditional houses. This road leads up the mountain to a spectacular alpine highway, known as the Bukak Skyway, with an observatory at the summit offering Seoul's most breathtaking views. At the end of the winding road are Mount Inwhang, popular with hikers, and Kuksadang, a village of shamans' shrines and tiny temples clinging to the slopes. Higher up, you may see a shamanistic good-luck ritual - or even an exorcism. All within a brief drive of Seoul's central business district.
Ten years ago, Seoul didn't have a park worth mentioning. Today, halfway up the slopes of the landmark Mount Namsan, across the road from the Hyatt Hotel, is a park that offers challenging jogging tracks, a wild-flower garden and great views over the metropolis and down to the river. Another huge park stands in the centre of the financial district. It was the city's first airstrip, then a helicopter evacuation zone for the nearby National Assembly in case of war. It now offers plenty of green space, so-called acupressure footpaths, and in-line skating tracks. The city's most remarkable park is Seonyudo Island. Formerly Seoul's waterworks, the entire island, including its concrete tanks, gantries and pumps, was transformed into a park in the run-up to the 2002 World Cup.
8 National War Memorial
Although it now faces competition from the enormous National Museum, which re-opened last year, the memorial's main exhibits focus on the landmark event that still defines the country for many foreigners: the Korean war. Outside the museum are aircraft, tanks, artillery and even a submarine. Inside, along with Korean war exhibitions, are halls dedicated to Korean independence and South Korea's experiences as a US ally in the Vietnam war. Military bands and drill teams often demonstrate in front of the museum, which is next to the Yongsan US Army base and opposite the Ministry of National Defence.
9 Non-verbal performance
South Korean films, television series and pop bands continue to be popular around the region, but in Seoul your best bet for a live show may be one of the non-verbal performances that have gained a mass following in recent years. And being non-verbal, they present no language barriers. The most popular, Nanta, is a zany comedy set in a kitchen and enlivened by neo-traditional percussion skills. Tokkebi Storm is another percussion-based piece, featuring tokkebi, or Korean goblins. Jump is a spectacular slapstick show about a family of bickering martial-arts experts. All three feature high-energy, physical performances, lots of noise and plenty of laughs, but beware: audience participation is part of the fun, and foreigners are favoured victims. Check with city tourism booths or your hotel concierge for times and venues.
Can a stream win a mayor the presidency? The mayor of Seoul, Lee Myung-bak, hopes so. He chose the US$350 million restoration of Cheonggyecheon stream, completed last year, as his flagship environmental project. The project has proved a hit with citizens, and you can see why. Lee tore down an overhead road to transform the 6km stream, which was essentially a covered drain, into its present glory. Running through the downtown business district, it is crystal clear (albeit only 32cm deep) and attractively landscaped, with 22 bridges and paths along both banks. It has a series of fountains in the plaza at the end, and at the head of the stream a few bars and restaurants are pioneering what may become a welcome new Seoul trend: riverside cafe culture.