Naejangsan is one of the most popular places for outing and hiking during autumn in Korea. I think that the easy 2.3 km long flat walking path filled with maple trees is the main reason. It is a really nice walk in the shades of maple trees and there is a small stream on the side.
At the end of the 2.3 km road/path is the beginning of some new routes: cable car up to the view point on top at an additional cost (not included in your entrance ticket), walk further to the Naejang Temple, and there are several hiking trails you can go further up the mountain. Depending on your time, most tourists won’t go on further hike because many of them come to Naejangsan from Seoul on a day trip. It takes about 3 hours one way. And the sun goes down after 5pm.
The first time I visited a few years ago was the best. It was less crowded. You could sit and take pictures everywhere and walk to the wooden pavilion in the Naejan Temple. Now, the road is busy with many shuttle buses and cars. Grass areas and trees are mostly barricaded. To me, it was too crowded even on the week days.
Travel tips: try to stay in Jeongeup or Naejangsan for a night and go the national park early morning and avoid the weekends.