What about Courtyard?
Looked at both Plaza and Westin. Problem is we are traveling with our adult daughter (3 adults in the room) - so Plaza doesn't have rooms that accommodate 3 and Westin does it for ~$100 extra ($80 extra adult and $25 rollaway).
Having discounted these - what about Courtyard Namdaemun? it is manageable $20 for 3rd adult and based on google maps, it is 9 minutes walk from there to Plaza.
AX