The core attraction of Nam Phong National Park, and the nearest nature to Khon Kaen city, the Hin Chang Si ('Elephant-Rubbing Rock') area is full of oddly eroded house-sized rocks scattered around a scraggy forest. There are some wonderful viewpoints of Ubonrat Reservoir and the Phu Wiang Mountains. It's worth spending at least an hour roaming around here, and you could easily do more if you follow the trail northeast along the top of the cliff (you're supposed to hire a ranger for this).
A small rock-climbing community (www.khonkaenclimbing.com) is active here and hosts a bouldering festival in January. Isan Explorer has a trekking trip that takes you from the top of the mountain down to the lake below.
It's 50km from the city and there's no public transport anywhere near it.