T.S.
I can't speak specifically about schools, but Fairfield and Vacaville both have nice areas. Vallejo is the city you want to avoid, high crime, gangs, drugs, bad schools, the city has even filed for bankruptcy, NOT a good place!
Benecia may be a good choice, better schools but a longer commute. The newer part of El Sobrante is nice, and Crockett and Rodeo aren't too bad either.
You're in for a major culture shock, the Bay Area is crowded and expensive. For sure RENT before you buy, even if your child ends up having to switch schools, it will be worth it in the long run. It's going to take some time to figure out where it is you want to settle.
Good luck!