~15,000-50,000 won
Staying near home, having a bottle of soju or two, and dinner can be quite cheap for me. However, I live about 5,000 train ride from Daegu, so there is about 16,000 just in cab/train (cab is usually split, so about 12,000). There, I usually spend about 10,000-20,000 on food throughout the night and 5,000-20,000 (bottle of soju or a couple cocktails). Resulting in 30,000-50,000 in one night.
Factoring in a place to stay for the night (I usually just take the first morning train home) could add about 15,000? So on the expensive side... 65,000.
I'm assuming these costs will likely skyrocket in Seoul and maybe Busan up to about 100,000/night.