Skimming the health department web sites of various counties, it doesn't look like it. Most of them just provide the basic cases and deaths numbers. Whoever compiled this at the Stanford Open Data site (https://opendata.stanforddaily.com/#/datasets/covid19_bayare...) might be doing so manually.

SF County - https://www.sfdph.org/dph/alerts/coronavirus.asp

San Mateo County - https://www.smchealth.org/coronavirus

Alameda County excluding Berkeley - http://www.acphd.org/2019-ncov.aspx

Berkeley - https://www.cityofberkeley.info/coronavirus/

Santa Clara County - https://www.sccgov.org/sites/phd/DiseaseInformation/novel-co...

Marin County has an (ominously named) dashboard - https://coronavirus.marinhhs.org/surveillance

That would be so useful to identify hotspots within counties. Also information about new cases such as if they are working from home or are considered "essential workers". How are transmissions occurring despite all the stay at home efforts? That would help us all tighten up our collective defenses. Hopefully the governments are doing at least some rudimentary "contact tracing" efforts and we're just not getting to see the data.

Austin has a decent breakdown here: http://www.austintexas.gov/covid19

Not that I am aware of. And the counties vary a lot in terms of the data they provide. The best is Napa County.