Hi Mary,
You'll love Sydney! How exciting!
I used to work in north sydney - it is a great place. Very quiet on the weekends though!
Areas that are close to North Sydney are - Cammeray, Neutral Bay, Cremorne, Mosman, McMahon's Point, Waverton, Crows Nest. These are all great places - close to the harbour and lots of things to do. If you are looking at living somewhere slightly more 'suburban' Mosman is nice, but more expensive. Balmoral is close to Mosman too, but again, probably more expensive. You could also look at Lane Cove, Willoughby, Chatswood for more 'family' places - depends on what age your children are. If you really don't need a huge house and a true suburban area, the other areas are fine. Neutral Bay, while very nice, would have a higher incidence of crime - not serious stuff, just car damage etc.
If you need to look at locations, try
www.whereis.com.au - it shows the distance between areas. So, if you were considering living in Mosman, you could measure the distance to North Sydney.
All of those areas are pretty easy access to North Sydney - Chatswood would be on the train line. Most of the others is a quick bus trip.
If you need to have a look at properties to rent, or get an idea of what is out there, you can look at
www.domain.com.au
Our department stores stock plus sizing - there would also be a couple of stores in Chatswood I think.
Hope this helps - feel free to ask me any more questions.
Cheers,
Brooke
Temporary relocation to Australia 
