Can't go wrong with bibimbap, bulgogi, and dumplings! Make sure to pickup kimchi, too. Some people might not initially like the taste of it but I think it's delicious.
Once you're more comfortable with the food, I definitely recommend the pork kimchi stew (kimchi jiggae), samgyupsal, or bibim naengmyun, or really any soup.
Doesn't hurt to try their fried chicken, too! Especially if they serve it with pickled radish.