I am not a Mum but had lived in Sydney for 18 years (1994-2012) and graduated from Sydney Uni (B.Comm) and UTS (M.Bus). Lived in North West part of Sydney and went to Pymble Ladies College. I wasn't quite academically smart enough to go to the Selective High Schools, plus my Mum thinks if you need coaching to get into selective high school, then it's probably not right for you, but we were lucky, my parents can afford private schools.
Feel free to ask questions.
If you are looking house, in Epping/St Ives/ Chatswood/Strathfield, all house prices over $1mil. Use http://www.domain.com.au
For education purposes, for primary schools, Epping, St Ives and Chatswood will have better schools. Strathfield is hard as it has a mix of nationalities, the crime rates are higher but public transport is easier as Strathfield is a big interchange train station for north, west, part of Sydney. Note St Ives is not on the train line, you have to drive to the train station, so I suggest you pick Gordon instead.
In secondary schools, one of the best high schools is Killara High and Cherrybrook Tech, for single sex it is Epping Boys, Cheltenham Girls etc. Refer to this ranking list: http://bettereducation.com.au/results/hsc.aspx
St Ives and Chatswood is consider Upper Northshore and very middle to upper class with houses well over $2m. A lot of Asian parents there send their kids to selective high schools and private schools, because they are better off. Upper Northshore area also has some of the best private schools in Sydney.
Epping because of the new train line connecting to Chatswood, I assume house prices are also accelerating.
With a $700k budget, with levies and fees, I would say you can only afford a smaller house or an apartment, I think try Epping and the near by suburbs like Eastwood or why don't you consider north west Hills District, much lower crime rates, like Beecroft, Cherrybrook. If you want the Upper North Shore, the most affordable would be Waitara, Deniston or adjoining places like Lane Cove. In Australia, I would say try to buy along the train lines - refer to this http://www.sydneytrains.info/stations/pdf/suburban_map.pdf
For investment purposes, Epping, Chatswood, Straithfield will return ok. For Secondary school, even if you don't get into private schools or selective schools, I think Epping or Chatswood or St Ives is a lot better as Strathfield there is a bigger mix of students and a lot messier. Refer to this website for which public primary and secondary school you child might attend: http://www.schools.nsw.edu.au/gotoschool/index.php
I am making a generalisation here but the fact is, Sydney is based on MONEY, new money vs old money.
If that suburb has private school over $15000, it is probably a well-to do suburb.
Sydney North West- middle class, new money and mix of Asians and whites.
Sydney Upper and Lower north shore - Middle to upper class - mix of new/ old money, lower north shore more posh
Sydney inner west - Mix of classes - mix of new/old money, higher crime rates and different nationalities too.
Sydney East- Old money, upper class and less Asians. if the suburb is like ends with a "bay" then it is quite posh.
Sydney West - Lower to middle class depending where you live, but lots more "white australians" live out there.
Sydney Upper vs Lower South. - The Upper south has more Asians and Lower South also know as "The Shire" is very white.
For Asians, we do tend to stay together, I remember when we migrated in 1994, we lived in West Pennant Hills, there were not that many Asians, now ALOT of asians, especially in Cherrybrook due to its outstanding high school. End of the day, I truly believe that Australians in general are kind and loving people, very accepting of new cultures. Also they do help parents out a lot when your kids settle in earlier.
One piece of advice for parents and children alike, Australians LOVE sports. To mingle with the "White" Australians, you have to love sports. My brother went to Australia when he was 5 and he loved sports and he is more "ABC" then me, as I went when I was 9. But in the end Asians (Koreans, Indians and Chinese) all place academic pressure and there are tonnes of coaching colleges like Kumon, James An, Prior, North Shore etc etc. Those mums pressure like crazy. I am VERY LUCKY, my mum never pushed me and my 2 siblings.