There are several North Korean-operated restaurants in China, and quite a few in Dandong itself! You can recognize them by the North Korean and Chinese flags over the entrance. They are staffed by waitresses from North Korea who put on karaoke dance shows, and offer a variety of Korean and North Korean specialties. A great North Korean experience!
Favorite Dish: Pyongyang naengmyeon(Chinese: lengmian or cold noodles) are a North Korean specialty. They're buckwheat noodles served in a cold and tangy broth, garnished with marinated meat and Korean pear. A refreshing treat for the summer.
Kaegogi(Chinese: gourou or dog meat) is available at almost any Korean restaurant(North Korean or not) in China. I didn't try the dog meat here, but in another Dandong N Korean restaurant. It was served cold, and quite flavorful. A special experience!
There is a brewery in town, if you're the type that likes to sample local beers around the world. The name of the local beer in Dandong is "Yalu River Beer" and I can not confirm if the ingredients actually include any drops of North Korea's territorial waters.
The Chinese toast with the words "gan bei" which in English would sound exactly like "gone bay" and it means "dry glass" so you are supposed to empty it in front of your Dandong hosts.