Inwangsan is a 336-metre mountain west of central Seoul, close enough to the palaces to fit into a city day but steep enough to feel like a real climb. Trails pass Inwangsa temple, the shamanist shrine of Guksadang, rocky ridges, and stretches of the old city wall.
The reward is one of Seoul's best close-in views, with Gyeongbokgung below and the city spreading out around the hills. Wear decent shoes and give yourself time; the mountain is modest, but the paths can be rough.