Sutter Health Fremont Center
This is probably a bit far for you, but we really like our son's pediatrician in Fremont. Dr. Jamilah Friday. She's African American, we're not. We used to live in Oakland, and then Hayward, and now we live in Berkeley, but we still go to her almost 4 years later because she's just very good at explaining things, taking her time, giving good advice (especially for us new first time parents).
The nurses are also really good. They're lightening fast with the shots, my son doesn't even have time to cry. Haha.
Besides the distance, the other drawback is that it's almost impossible to call the office and talk to her right away. There is a "care team" of nurses and assistants who take your message and then she'll call at the end of day. She does respond to emails, though.