Hi juliap
Where are you moving from? Are you moving from the UK? Sometimes Brits may be confused because public schools there are more like what we call private schools. Government run schools are called public schools here.
I went to a government primary school. I can say that the public primary school system here is really very good and there seems to be little variation from school to school, or area to area. For some more objective advice, there is an excellent article at this link:
www.schoolchoice.com.au/nsw_public_schools.
Many parents only feel the need to pay for tuition at the high school level because of this fact.
North Sydney is, as you are probably aware a city suburb as well as a general term used to describe areas north of the CBD. It has a large range of boys, girls and co-ed public schools.
While it is true that schools require that their students come from their local enrolment area, principles sometimes have some discretion depending on available resources. For this reason, it is a good idea to do some research. If your kids have special needs, this may be really important.
There is at least one local company that I know of that will help with the task of researching local schools. They can help with other things too, so if you would like some further info, or just want to chat, please get back to me.
Good luck
Luke
