There are a number of water-front canal towns around Shanghai, including the one where they filmed Mission Impossible 3. Some are more touristy, some less. TimeOut Shanghai compared them here. Whichever one your decide to go to, don't go on a weekend or holiday.
I went to Zhujiajiao, which is accessible by public transit. The buses leave from just south of the Shanghai Museum in People's Park, via pink buses bearing the destination "朱 家角." Google says the trip takes two hours, but it's really about an hour and a bit each way. You stay on the bus until the last stop.
In many ways Zhujiajiao feels like a Chinese version of Brugges, but even more touristy. I imagine it would be terrible to visit on a weekend, when many Chinese would also visit. And make no mistake: most of the tourists you're likely to encounter anywhere in China will be Chinese tourists. They are greater in number and have more market power (at all spending levels) than foreign tourists.
|Map of the tourist area at Zhujiajiao|
Yuanjin monastery from across the Chaogang river. Yuanjin is the most photogenic of the religious sights.