Similar situation....here's what the Westin suggested for me later this month...

* Seoul city tour bus trip :

Night course ( 19:50,20:00 dep.)

no need to book, ticket can be purchased on the bus

you will visit and see Seoul tower and night view of Seoul

* Sanchon (performance and dinner) :

temple food in Insadong(antique street)

* Shopping at Dongdaemun market

Fashion market which open till 4 a.m.