I live right at the base of Namsan Mountain, which is basically right in the center of Seoul. The mountain has an observation tower on top which is a pretty big tourist attraction, but I still haven't gone up it. The views from the mountain are pretty spectacular, and it's a great place to run.
It's not easy though!
It's about 3 miles from my house to the top of the mountain (and I take a shorter way home). I don't know the elevation gain, but it's a lot! My calves were really sore going up, but after stopping to stretch, they were fine.
The views at the top weren't as great as I was hoping... too much air pollution (sorry, lungs). But it was still a really good, tough 49 minute run!