There are plenty of good local restaurants and street food.
Food stalls. For a variety of snacks and dishes, try the food stalls opposite the Id Kah mosque. The stalls start operating during the evening.  edit
Sunday Market. The Sunday market also has good things to eat.  

It may be wise to avoid anything with ice as the ice in Kashgar is usually carried in large blocks and frequently placed on the ground so they may not be clean. During the summer months there are huge heaps of melons and watermelons - cheap, tasty and refreshing. The going price for a hami melon) is around ¥1 per kilogram, so in total, it costs ¥2-5 per melon depending on the size. Buying, washing, and cutting it yourself is probably the most hygenic way to eat these fabulous tasty fruits. If you are staying at a hotel, you can also easily buy a simple cutting knife at any of these markets for about ¥1-3 as well so you should be all set.

Altun Orda Restaurant is the local restaurant with reasonable prices. It is not only good place to taste some local dishes but also to see the local architecture of Uighur people. Try the specialty pollo or rice pilaf with raisins. Tel: +86 (998) 2583555

Karakoram Cafe, 87 Seman Road, Tel +86 (998) 3422888. Western style. Quality food, hot drinks and service that speak English, this may be an oasis in the middle of hectic Asia. Prices are a little pricey but if you can afford it, it is worth it.

K2 Rooftop Cafe, Rd Nuo'er Beixi (Right to the North of Id Kah Mosque), Tel +86 (998) 2823376. Western style. Fine coffee& pizza, iced drinks, dessert and waiter that speaks good English, the terrace that covered with plants has great view of the mosque and the old town. The cafe is within the Kashgar Pamir Hostel.  

Shawarma (Continental food), 110 Seman Road (Just north of Eden Hotel and Fubar on Seman Road). Owned and run by a native Pakistani, this is the place to get home-made Pakistani food in Kashgar. Serving mostly daily specials, such as a spicy ground beef platter or curried chicken, the taste of the food is impressive. Ask politely in advance to have delicious falafel or hummous made to order. 10-20 Yuan.

Yasin Kariagim Silk Road Uighur Restaurant, Kumudaierwazha Road (Just off the main old city shopping road that runs up the west side of the Id Kah Mosque),  2820008. Popular among the locals, this place serves very fresh meat. In fact, sometimes they have no more meat to offer because they've sold out. Buy a nan bread fresh out of the oven from one of the many local bakers on the side of the road and bring it with you. Get lamb skewers and liver skewers and enjoy it with your nan bread. 10-20 Yuan.  

Drink
There are not as many places serving alcohol in Kashgar as in other areas of China.
John's Cafe, (In Qiniwak Hotel (ancient british consulate)). Offers backpacker hospitality at 1.7 times the price of other locations, and is very popular among single travellers. Managed by Jack who speaks fluent english. Seems to be closed in the off-season