If you have a couple of hours to spare, or a few minutes a day for a while, learn to read and write Korean (Hangul). This is a good place to do it, plus here for the stroke order. You won’t be able to understand anything, of course, but being able to at least read out anything you encounter written in Korean seems like a pretty good payoff for a couple of hours work. A bit longer, maybe, if you want to remember it long term, but it really isn’t difficult. At least, after however many hundreds of hours spent becoming moderately competent at reading and writing Chinese, this seems like a pretty decent time investment/reward ratio.

(If you’re linguistically inclined, you can also hit up Wikipedia and read about how utterly awesome the Korean writing system is.)