Where can I find affordable rent in San Francisco for a family with two young children?

Padmapper.com is the best alternative to Craigslist--its mapping function makes life a lot easier. The only problem is the there are fewere listings since Padmapper and Craigslist got in tiff a couple of months ago. You might also try a website like Trulia--though they are mainly for buyers not renters.

As to places to look, I would try the Sunset District and West Portal, relatively affordable in spots and away from the crime and other problems you'll find at the heart of the city. (If you really want to save money though, you best bet is to try South San Francisco and to commute into SF--cheaper, okay schools and not bad in terms of crime.)

Good luck.