I've sold homes in San Ramon for 15 years and have not come across any below market rate homes. There are below market rate homes in nearby cities however including Dublin and Danville. In fact, Danville has a new development on the westside close to San Ramon which has BMR properties. Danville is in the same school districst as San Ramon so the schools there are highly rated. Hope this is helpful.
Here's a link: http://www.ci.san-ramon.ca.us/housing/images/housing05-05-13.pdf
City of San Ramon
Planning Services Division
2401 Crow Canyon Road
Let me know if I can be of further assistance to you Bianca, whatever your needs are.
However - there are homes in San Ramon that are more affordable than you may think. They may not be single family homes, but there are some large condos and townhomes available.
If you really want to live her - find a hungry agent that is willing to work hard for you!