갈비 (GALBI) is one of, if not THE BEST dishes that you can try while you're in Korea. But it's certainly not cheap.
Of course, all kinds of Korean BBQ are worth trying. And there are a lot of kinds you can try, including 삼겹살 (SAM-GYUP-SAL), 보쌈 (BO-SSAM), and others. This dish is on the next level above everything else.
The smoky flavor you get from the meat, the varied and beautifully-arranged side dishes, the fancy atmosphere of sitting at a table in Korea and having the meat cooked for you (instead of cooking it yourself), and the dipping bowls you get for adding an extra bit of flavor to your meat. All of these combine together to create one of the best food experiences that you can try while visiting in Korea without burning a hole in your wallet.