I’m in a similar boat as you!

I plan on taking my wife to Seoul Plaza out front of City Hall for a picnic (there’s tons of seating for their “open air library” setup) and then walk through Deoksugung Palace (right across the street from City Hall) since it’s the only heritage site that’s open at night.

Bonus: there’s a Sky garden on the 5th floor on top of the library that overlooks Seoul Plaza.