The pair listened intently as a guide showed them around the capital's grandest palace, Gyeongbokgung, on Tuesday. Despite the damage suffered during Japanese colonial rule, surviving structures such as the 48-columned Gyeonghoeru pavilion still have a majestic appeal.
Nearby is the National Folk Museum, which recreates everyday life in Korea from the 14th century onwards and features a display of kimchi - the Korean national dish made of fermented seasonal vegetables.
In contrast to the pagodas, pleasure gardens, temples and palaces of the historical centre, the other side of the Han River - where the island of Yeoui-do is Seoul's equivalent of Manhattan - offers a very modern cityscape.
The royal duo are also set to visit Busan, the country's largest seaport and home to a bustling fish market. To get their bearings, they could do no better than to take in the views from the top of the Busan Tower.
Other attractions on the southern coast include the nearby beach resorts of Haeundae and Songjong. While for something a little more traditional, many visitors take in the hot-spring resort of Tongnae, alternatively nature-lovers will find plenty to distract them in the 1,000-plus islands that make up the Tadohae Haesang Marine National Park.