This is one of my favorite entrance of Bukhansan mountain. As the mountain is located Northern part of Seoul, there are many access points in the City. For me, I prefer to use entrances near the government office building which is for the five North Korean provinces. The hiking route starting from the Gugi-dong points are well managed and adequate for about 4 hours' hiking. Also you may find nice Korean restaurants near the entrances which will give a good time for rests after lots of sweating!
139-22 Gugi-dong, Jongno-gu, Seoul, South Korea