On the Peninsula, Belmont is popular with renters. Lots of tech guys there. Also Millbrae. Both are within striking distance of South SF. The problem is even a studio apt. may start at $2k/month.
I would not recommend the East Bay (Oakland, Hayward, Union City.) Crime is higher and it can be a culture shock. Plus the commute would make you want to kill yourself.
In Contra Costa, Walnut Creek and Pleasant Hill have a lot of rentals, plus they both have a BART station which can be great if you work close to BART at your destination or there is bus service to take you where you need to go. Walnut Creek is the better of the two as far as shopping and eating go.
All in all, it's going to be a pain in the ass to get to work if you have to cross the bay. If you drive, that means a bridge, which sucks. If you take BART, not as much a problem unless there are no BART stations or bus routes near your workplace.
Oh, no matter how cheap the rates, don't get suckered into place like San Pablo, Oakland, Hayward, Union City on the east side of the bay (The East Bay) or the "flats" of San Mateo or Redwood City on the Peninsula (near the railroad tracks.) They may be cheaper, but crime can be a problem (Especially the East Bay. Check out the Milo riots and all the BS that anarchists pull in Oakland.)
Oh, the Serramonte section of Daly City is the closest to your wife's workplace. It's foggy and cold there in the summer and depending on one's racial sensitivities, it's not for everyone.
If you were to ask me as a middle-aged White man where I would live, I would go for Walnut Creek or Pleasant Hill. Both cities have a BART station and if you can drop off your wife and pick her up after work, BART is perfect (parking at BART can be difficult, depending on when you get there.)
BTW, just west of Walnut Creek are Lafayette and Orinda. They also have BART stations, but are considered upper-middle class and as a result, somewhat expensive places to live. I used to date a girl who had a nice apartment in downtown Lafayette. Nice area and I can't imagine she had any money, so maybe it's doable. It has kind of a small town, country setting in some ways. Both Lafayette and Orinda are very nice (Lafayette has a bigger downtown) and about 45-50 minutes to South SF I would imagine (on BART).