A friend of mine has a wife and kid ... paying 3500 a month for an average place in Mountain View (2 bedrooms). I'm paying 2500 for a 1 bedroom and am considering finding roommates (in my late 30s .. shesh). You could try renting someone's basement ... nice deals are hard to come by but you might get lucky.

Also consider living a bit further away (Santa Clara or even San Jose). Traffic sucks but it is a necessary evil. You might be able to get a decent 2 bedroom for 2500. Make sure your wife has immigration status that allows working else you will be screwed. I have many friends who had highly educated spouses who ended up sitting at home for a year+.

Edit .. some more additions. I don't want to scare you but want to give you some data.

1) Make sure you budget for a car. While uber is awesome, it is very hard to live here without a car. Everything is sprawled out. A cheap car isn't great value ... you end up spending 20K on a car (you recover costs when you sell it of course).

2) Make sure the uni covers health insurance for your whole family ... it is often a payroll deduction so find out how much they charge.

3) East Palo Alto is dangerous so don't go there.

4) I eat out all the time ... food is not as expensive compared to Europe. With a kid, eating out probably isn't a good idea though. Consider shopping in bulk at Costco (need a car for that though).

5) I see posts on craigslist about professional couples who want to share a house. I hope you get lucky and find one of those situations. Seems like a good option.

6) Find out if the uni has subsidized housing. UCSF does and offers it to post-docs. That can be an amazing deal.

Best of luck to you.