One of the little nightlife gems of Cheonan is Caliente Bar. Warming and welcoming to everyone, they have an excellent clientele and great events from dance classes to open mics. This is a great place to go when you are looking for local, fun, comfortable and inviting. You really need to hang out here at least once.
The other benefit of going out in Cheonan, if you are from Pyeongtaek, is that they have late trains coming back past midnight. It's a much better option than Seoul if you are looking for a fun night out of town. In a pinch, you can even catch a taxi back to Pyeongtaek for about 20,000won.