Probably the one Xi'an food that people throughout China have eaten, whether they have actually been to the city or not, is 羊肉串 (yáng ròu chuàn). They are sold in night markets everywhere in the country - China's most ubiquitous street food. They are lamb/mutton kebabs. Who doesn't like food on sticks? When I lived in Xi'an there was nothing I liked better of an evening than to go out, either alone or with friends and find a street stall selling Yang Rou Chuan. They weren't hard to find. See the last Chinese character in the name which looks like a kebab! They are available in some restaurants, but are more commonly found as street food. Bite size pieces of mutton (fatty tail meat is the prime choice) are threaded on sticks and grilled over charcoal while being sprinkled with cumin and chilli. They will omit the chili if you are not a spice lover. Me, I ask for extra! It is astonishing how many of these you can get through on a warm summer evening in the open air, washing them down with a cold beer in good company.
Some stalls sell only these; others also offer alternative meats such as beef or chicken and also sheep offal. Due to Xi'an's large Muslim population, pork is rare. Outside any of Xi'an's universities is a good place to look for kebab stalls and they are often cheaper than in the touristy Muslim Quarter. I regularly ate them for a year at the same stall beside Northwest University near the South Gate of the wall. Cheap and cheerful.