You are right to be concerned with crime in Stockton as it seems to be getting worse in some areas. Although never immune from crime no matter where you live, I believe there are some very good areas to live in Stockton. To name a few:
Lincoln Village West
For the most part these areas are safe and are good communities.
For more information check out this new tool from the city of stockton, which maps crime calls in differnet locations. Although, I must say this site is not always functioning. Its hit and miss.