The water served in restaurants is always boiled. Since even the Chinese do not drink the water, there is not a question as to whether or not to boil it; this is just a matter of course. Similarly, if you ask for ice water, the water used to make the ice will be boiled prior to freezing. Dispensers in airports and railway stations also serve boiled cold, and sometimes hot, water.
With respect to showering, washing your face and brushing your teeth, most reliable sources state that this is ok. Local Chinese do this. When I go to China, I use the tap water to brush and wash. I tell travelers that it is fine to do so, however, if you have concerns, you can just boil water in your hotel room and use it to brush and wash. Alternatively, you can use bottled water, although that is a more expensive option. The CDC states that it is best to avoid swallowing water while showering, and depending on where you travel (rural locales), using boiled water to brush.
As with traveling to any third world country, there are small annoyances that we must bear. However, if we only visited places with the same creature comforts as home, we won't open our eyes to how most of the world lives. The tradeoff is clearly worthwhile.