Many men come to Shanghai on business trips and while the need for suits, at least in the US, is not as great as it used to be, you still might want to check out a tailor while visiting China.
W.W. Chan is a tailor outfit based in Hong Kong with a shop in downtown Shanghai. Known locally as one of the best tailors in Shanghai, many men both foreign and local get their suits made at W.W. Chan. Most of their fabrics are imported but the labor is the key to getting a great suit made and this is where Chan excels. The price you'll pay for a custom-made suit of Italian fabric will run around the same price you might pay for a department-store off-the-rack suit in the US; however, it will be a fraction of what you'd pay for a custom-made suit of imported fabric at home.
Even if you don't need a suit, you can have shirts (both casual and dress), pants and khakis, and business casual jackets made. The tailors at Chan take your measurements and keep them on file. So when you love your shirts and want more, just phone them up from the US or Europe and work with them to have new ones made and sent over.
While not the least expensive option for custom tailoring in Shanghai, W.W. Chan is one of the best. Expect to go in for at least two fittings for suits. If you are short on time, they can rush orders. Your best bet is to go in during weekdays (they're open late) and take your time. On weekends it can be quite busy with long waits.
W.W. Chan & Sons Tailor LTD
See their website for current list of locations and operating hours.