I would definitely vote against Hayward. It is an industrial area and not particularly nice in my opinion. I have spent some time there for business reasons and all the people I know who work there don’t live there nor would want to.
I also agree commuting via car in the Bay Area sucks. I’d go with south SF or somewhere on the BART line.
Some friends who work in south SF rented a large million dollar home in San Mateo for about $3500/month and then later bought in Foster City and are very happy with Foster City for raising kids. They paid in the low 800s for a 4/3,~ 2200sq ft. Perhaps try renting in those areas before deciding?
