If you want to avoid the typical Western tourist areas and go shopping where the locals go, head to Song Xian Qiao Art and Antiques market, which is the second largest antique market of the country. The entrance - with chipped and peeling walls and quiet dusty shops - may not seem inviting but inside there are about 500 to 800 vendors selling everything from handicrafts, antiques, Shu embroidery, old porcelain dishes, painting, calligraphy, Shu silks etc. Read more here.

Songxianqiao art & antique market, Chengdu 087 (Source: gill_penney)

The best place to shop for souvenirs is Song Xian Qiao Antique City, the country's second-largest antiques market, with more than 500 separate stalls selling everything from Mao-era currency to fake Buddha statues to wonderful watercolor paintings. It's near Du Fu's Cottage and Wu Hou Temple.

 (Source:  Fodor's Travel Guides)

As a bonus you can watch silk being extracted from silkworms and woven into silk at the nearby Jinli Street, which is East of Wuhou Memorial Temple, renovated to look like old China. (Note: You can also watch silk being woven into cloth near the Wenshu temple, which is not as big a tourist hotspot, so it'll be quieter, though the food is as good there.) You can also have your bust made out of clay by an artisan while you sit for him or her, or even have your ears professionally cleaned! This is something that hotels will do for you in Sichuan, but it's not something you usually find in markets. When you're done shopping, there are restaurants and excellent snack stalls selling local food. 

Here's a review - 

The good food stalls here make up for the fact that this is a very crowded tourist destination, popular with local teens and visiting Chinese tourists. Good people watching and snacking if you can ignore the crowds.

 (Source: TripAdvisor)

Address: Song xian qiao Market, 22 Huan Hua Bei Lu, Chengdu

Chunxi Road is the major downtown shopping district where you'll find more than 700 modern departmental stores selling brands like Lacoste, Nike, Polo, Gucci and boutiques, supermarkets and eateries (including the standard KFC, MacDonalad's, Pizza Hut and Starbucks). There are about 4 or more blocks of stores surrounding the road itself. The big departmental stores include Chicony, Parkson and the Japanese stores Isetan and Ito Yokado. If you find yourself lost, reorient yourself by starting at the central square with a statue of Sun Yat Sen. If you want cheap versions of big brands, you'll find it here, and some are excellent fakes. 

Downtown Chengdu Shopping District (Source: daniellinphoto)

Chunxi Road is the glitziest shopping district in Chengdu and, hosting a million people on summer weekends, definitely the most crowded. The stores here mainly sell brand name foreign goods or their Chinese counterpart. The street has been redeveloped around a collection of plazas that stretch out across three or four city blocks, with small sitting parks, high and low-class shopping districts, restaurants and bars, a well-stocked Ito Yakado, and hundreds of other shops.

 (Source: Chengdu Living)

Address: Jin Jiang District, Chun Xi Road

The He Hua Chi wholesale market on Bei Zhan Dong Yi Lu (or Bei Zhan East Road) is a paean to reasonable mass production which can be an attraction in itself even if you don't want to buy the stuff. At this wholesale market housed in the Futian building near the North Railways Station, traders collect to sell everything from household wares to clothes and shoes, and all of the shops are crowded into winding alleys. Be prepared to bargain a lot. 

 (Source: clurr)

You can have a good bargain for products at He Hua Ci District. Prices of one or multiple products can be bargained at this wholesale district. Since the shops are organized into categorized sections so the competition amongst the different shops is really very severe. Since there are an entire block of merchants selling the same type of products so you can easily bargain from one shop to the next for the cheapest product. While going for shopping in He Hua Ci District you should be aware of the fact that the merchants try to take advantage of the shoppers and specially the foreigners. So the advice is, when you go for shopping in He Hua Ci District you can 'shop till you drop' keeping in mind you get the best price.

 (Source: Shopping at He Hua Ci District)

Address: 4F, Futian Building, Beizhan Dongyi Lu

Hours: 9 am to 5pm

For electronics, the place to go to is Computer City or Digital City (here's a blog post on it). This huge arcade of 6 floors of electronics (which are divided into departments such as laptops, cameras, and even a recycled IT goods department on the top floor!) Prices are competitive since there are so many stores, but there's lots of scope for old-fashioned Chinese haggling. Walk into a few nearby shops and find out the prices for a product you are looking for to compare.  

Camera Store (Source: Helga's Lobster Stew)

Here's a review:

All the usual cautions apply while shopping in Computer City, where the sales staff can be quite aggressive. Bargaining skills are essential, and it pays to make sure what comes in the box they hand you is the actual make and model that you agreed to buy. Still, Computer City is a fascinating place for techies to spend hands-on time with the latest toys. Componets and accessories, cables, hand tools, and soldering irons are also available, and for very cheap, for those who wish to DIY. For visitors to Chengdu, Computer City is also a unique opportunity to check out many products and brands from Taiwan, Korea, and the mainland which may not be available in one's own country.

 (Source: More Chengdu)

Address: Shu Ma Guang Chang Square, at the junction of Renmin Nan Lu and South 1st Ring Road, in Wuhou district.