@Actnaturally I have had a quick look for you re hotels in Seoul but I will need to take a bit more time and come back to you - week days seems too short to get much done...
We now find an airport bus is super easy as there is a route that stops outside 'our' hotel near Gangnam (where DS lives). You literally wait at a bus stop, put the bags on the bus, sit back in a big and comfy chair and get dropped at the front door of the terminal. The subway is OK but not as easy as the bus, we are now converts as the subway always seems to need a change, and as in Japan the stations are big and a change is often a reasonable walk.
Top tip for both countries - check which subway exit you need to save yourself an unnecessary backtracking walk.
So in general, the area to the NE of Seoul station should be good, I'll look to see the exact routes but airport buses 6001 and 6015 seems to go to that area. On our first visit DS advised us to stay in the area as its a good location and he was right, as it offers easy access to Meyongdong, Cheonggycheon stream and Gwangjang market, Gyeongbukgong palace, Insadong and Jogyesa Temple and Bukchon Hanok Village. You also have the subways handy for the National War Memorial of Korea (an impressive indoor and outdoor collection and a War museum really rather than 'just' a memorial), and the beautifully curated National Museum of Korea (both free), Hongdae (where i feel old!) Gangnam and Jamsil and also trendy Seongsu.
I've added a map with the general area marked but I'll come back to you later with a more refined idea if you don't make choices in the meanwhile.
Do you have an idea of what do sort of thing do you want to see and do? Do you want food recommendations for dinner (love the food 😋)?