There is nothing cheap near the National Museum. You can go to the hutong west of Qianmen, where there are many small restaurants. If you don't mind fast food, you can go to Wangfujing. There are places to eat in shopping malls (don't go to Wangfujing Food Street, where things are expensive and boring)

There are no cheap restaurants near Junbo. You can go south and look inside the hutong in the east.