The National Initiative for Children's HealthCare Quality (NICHQ) has a website where you can find fact sheets about the state of children's health in each state. The State Fact Sheets provide the most recent national and state-based data regarding health in addition to childhood overweight and obesity prevalence from data collected in 2007 by the National Survey of Children’s Health.
For overall health in California the (2007) fact sheet suggests that compared to national averages, children in CA are:
less likely to be in excellent or good health;
less likely to have excellent or good oral health;
less likely to be adequately "engaged" with school;
less likely to be involved in activities outside of school;
less likely (ages 0-5) to have families that read to them;
more likely to have missed 11+ days of school in the past year;
more likely to have ever been breastfed; and
less likely to watch more than one hour of TV a day during the week.
In relation to obesity, 31% of all children in CA are considered obese or overweight, and 33% of low-income children age 2-5 are overweight or obese. There are 8% of children ages 6-17 who spend 4 or more hours a day in front of a (TV, video, or computer) screen during the week (which is actually lower than the 11% national average).
I cannot say that it is a pretty picture at all, but CA is one of only two states requiring nutritional information in restaurants, so there is hope!