Night market:
Xi'an has a wonderful night market near the central mosque that is a must-visit for a Chowhound. They have loads of stalls with interesting and unusual foods, including loads of good sweets that are sort of reminiscent of Middle Eastern things, with a lot of honey and sesame. Also, be sure to try bian bian mian, which you can find pretty easily if you look for what looks like the most complicated Chinese character you have ever seen. Also in Beijing be sure to have chuanr, skewers of lamb and other things that are cooked over an open fire. And visit the stretch of Dongzhimennei referred to as "Guijie" for hot pot and crawfish in hot and numbing sauce.