Be aware that local hotels in China can have shocking food handling practices. For that reason, I stay in major American chain properties.

Don't even think of drinking tap water, brushing your teeth with it, etc. The cost of bottled water at convenience stores, which seem to be everywhere, is so low that it's not worth the risk, even if a place tells you that the tap water is purified. Nicer hotels provide a lot of bottled water every time they service the room, although the stuff in the minibar can be expensive.

Just be aware that a few tourist places do not allow you to bring in water. This happened to me at one museum in Shanghai on the Pudong side and also at Shanghai Expo. Sometimes an unopened bottle of water is permitted but not one that has been unsealed.