Thankfully despite Seoul’s war-torn past and rapid development, there are still quite a few visible reminders it was once the seat of power of the Joseon Dynasty, which ruled the Korean peninsula from the 14th through the 19th centuries. Changdeokgung is arguably the most atmospheric of the city’s former royal palaces and most sublime expression of Joseon-era architecture. When you’re done there you can explore the winding alleys of Bukchon, a neighborhood just west of the palace that was home to much of the city’s aristocracy and still has one of its highest concentrations of hanok, or traditional Korean houses.
It can get pretty crowded during rush hours, but nothing beats the subway in terms of convenience, cost and coverage. That said, taxis are also very affordable by global standards and are a good travel option, particularly outside peak traffic times or if you’re traveling in a group.
At least one of the city’s palaces—Changdeokgung or Gyeongbokgung are good choices—as well as the War Memorial, which has one of the world’s best collections of vintage military equipment and is a poignant introduction to the conflicts that continue to haunt Korea to this day. The Insadong shopping street is a good one-stop destination for local crafts and souvenirs, and the massive National Museum of Korea shouldn’t be missed by anyone with an interest in Asian history or art.
Seoul’s one of the few lucky cities that has (part of) a national park within its limits. Bukhansan National Park is accessible by subway and includes a rocky mountain range that offers some serious challenges for avid hikers and rock climbers, as well as easier trails, temples, and fantastic views that will also be appreciated by casual visitors.
There are a lot of exciting things happening in Seoul at the moment food-wise. The Gangnam/Apgujeong area, south of the Han River, has become a hotbed for “new Korean” cuisine that updates traditional dishes with contemporary ingredients or culinary techniques, at restaurants like Jungsikdang or Star Chef. I’d also recommend trying Buddhist temple cuisine—purely vegetarian but by no means austere or dull. It has reached new heights at restaurants like Baru and Sanchon in the Insadong area. And for a more down to earth or nostalgic (not to mention easier on the wallet) experience, head to one of Seoul’s markets—Gwangjang or Namdaemun are among the best—and hop from stall to stall sampling the various snacks and rice wines on offer.
In all honesty I would probably direct them to Hong Kong or Singapore— despite a lot of electronics being produced here the goods available locally tend to be expensive and optimized for Korean users. The tech-inclined may nonetheless appreciate Yongsan Electronics Market, which covers multiple city blocks and offers just about every gadget under the sun. Negotiating is common and most vendors will readily reduce their asking prices or throw in a few free accessories, particularly if you’re buying multiple items. It’s wise to know roughly how much you should be paying for whatever you’re buying as overcharging is not unheard of.