Depends if you want to live close to Chinese community, if so, try Chatswood.
I think in general, the ranking of safty is Northern suburbs, then eastern suburbs, then southern, then western suburbs. You may like to consider the Hills district (Pennant Hills, Cherrybrook, Castle Hill, West Pennant Hills), these are popular northern suburbs that's not too expensive and v. safe.
Thanks for the information. 1 of my friend told me that Chatswood is a good place to live too, but I am afraid we can't afford the rent as we have 2 children, and only my husband will work.
Do you guys knows the price/rent range of the apartment in the northern area?
How old are you children? It sounds like living along the train line would be better for you. You might like to consider Hornsby as well. There are some newer apartments. (Hornsby is about one hour by train to the city).