It took a couple days to get into the groove and start to enjoy Seoul fully. But, once I got the hang of things, like public transportation, restrictions on foreign credit cards and foreign navigation apps; I found Seoul quite enjoyable.
But, it is BIG. It is the 5th or 6th largest metro area in the world, so a week just wasn't enough to immerse myself.
First, remember, this is primarily the center of government and commerce for South Korea. Tourism is certainly not primary.
But, there are some fascinating things to see and do.
The War Memorial of Korea remembers the history of conflict over the last 2000 years, with much of the museum dealing with the war that technically still continues with The North.
The National Museum of Korea is a very large complex that explores art, history, ethnography, archeology. Primarily of Korea and neighboring countries.
Heading up to The Seoul Tower gives you great views of the city, and offers many hikes through the huge park, as well as the old city walls.
But, the highlights of the city are likely the old Palaces, Gyeongbokgung Palace and Changgyeonggung Palace, as well as the Bukchon Village between the 2 palaces.
Yongsan Park Dragon Falls