Crime
Violent Crime
Chinese cities are very safe. Violent crime is very rare. Traffic conditions and health should be more of a safety concern to you than violent crime. There is more crime and instability in the rural areas of the country, but even there it is not any more dangerous than most other countries.
Theft
There are thieves in China, just like there is anywhere else. Try to keep your valuables in front of you. A money belt or money pouch that you can wear in front of your body would be convenient and relatively safe.