Indoors
In the rain, do not climb Namsan and do not walk Naksan. One indoor of four, not all four: COEX, DDP, Yongsan I'Park, Yeouido IFC. The one you pick is the day's axis. Set a leaving time, and do not add a second mall inside it. A palace day moves to the Folk Museum or the Palace Museum. Seochon moves to the Seoul Museum of History. Daehak-ro moves to a theatre or Hakrim Dabang. Seongsu stays inside a warehouse. Do not ride a loop of Line 2 just to stay dry. That glues Garosu-gil, Seongsu and Jamsil back into one day. When the leaving time arrives, exit. If the rain stops, do not spend the rest of the afternoon catching up on Namsan or Naksan. Those wait for a clear day.