Koreatown isn’t actually big enough to qualify as a town. According to Google, it runs from 31st to 36th streets, between Fifth and Sixth avenues, though I know of it primarily as a 32nd Street phenomenon.
Korean abounds there, on signs for shops, restaurants, and other businesses. Among the shopping and eating options is Koryo Books, a wonderful resource for people seeking books and magazines in Korean.
I used to eat semi-regularly at a Koreatown restaurant called Kang Suh. I remember the kimchi (not actually my favorite thing in the world, but I had a friend who loved it), and I also remember grilling deliciously seasoned beef and chicken on a grill stuck in the middle of the table. It was a dramatic food adventure.