Bukhansan National Park (Dobong Section) is located in the northern suburbs of Seoul. The highest peak, Daegunbong (or Daekundae, 836m), is an enormous granite summit that provides excellent views of the surrounding area (subject to weather and pollution levels). The walk to the top gets quite adventurous as you walk steeply up the smooth granite summit, inevitably queuing with many others on the narrow and precipitous sections if you do it on a weekend or holiday (as I did). But despite the crowds it was an excellent walk.
My photographs from the day were rather hazy with pollution, which is to be expected given the mountain sits in a metropolis of over 25 million people (though a bit less when I climbed it in 2005). The mountain itself is very attractive though, so there’s still lots to look at if you can’t make out much of the city and surrounds.
The national park is accessible at various points by public transport, so you can choose a one way route and still get home easily enough. I can’t actually remember what the route I took was, but it was a one way route with a temple at the end (perhaps from left to right in the Google Map below). Here’s some info on the park from Visit Korea. Whatever route you take there will be some steep sections, and it’s probably not great for those with a fear of heights. Nevertheless, I remember that some younger hikers were doing the walk in their flat soled sneakers, so it can’t have been all that hard. Perhaps at the hard end of moderate if you take a long route.