Tenderloin is a district inside of San Francisco. Urban and probably higher crime than what you want. Rockridge is essentially Oakland.
Concord is safe but hot. Good BART commute to the city, tho (one train). Same with Walnut Creek, but more expensive than Concord. Another city like Concord would be Pleasant Hill. Many parts of Alameda are nice, but you might be pushing your budget, and some parts are like Oakland (to be fair, the Oakland hills are beautiful, but likely outside your price range).
I'd look at Fremont, which is in the South East Bay Area, is cooler than Concord, and at the end of another BART line that goes directly to The City. Fremont also has strong Asian and South Asian communities. There are a wide variety of ethnic markets for those otherwise-hard-to-find foods, utensils, and spices and a wonderful selection of restaurants that have great food but aren't too fancy for weeknight dining.
Public transportation in the Bay Area is concentrated in the larger cities and along the BART line, tho. If you are more than a few blocks away from BART in the East Bay, you can expect to need a car, and are likely to need a car to go grocery shopping as well, due to the sprawl of suburban living that also makes it lower crime and quieter than The City. Many suburbs are large enough that it might be easy for a wife to become practically housebound without access to a car. Every place she might want to go might easily be too far to reasonably walk.
If you look at a map, Sacramento is way too far, though I have seen some people try to car commute from there.
Oh, and don't expect to drive into the city! Parking is a nightmare and very expensive. It's really easy to get towed or have your car damaged (or stolen) there as well. Best to expect to ride BART to a downtown SF job coming from the East Bay, and to use a car to get to BART, because the more suburban parts of the East Bay have unreliable bus service that tends to be ~ once an hour and not on time enough to use for work commute.