We have come to Auckland for a year and are living in a small place called Beachlands about 20 mins from south Auckland and about 45 mins to the city centre. As the name implies there are beaches here and it is a very family friendly area with lots of other people with kids. The nearest Catholic school is Sancta Maria in Botany which is about 20 mins away - I have looked at their website and they seem to take both boys and girls. The schools in South Auckland are apparently hard work for the teachers (although I'm not sure that they would be harder than Salford!) but certainly there are few social problems in the area where we live (no burglaries in the area since at least Dec when we arrived), kids are polite, walk to school alone even when very little and freely play on the streets.
It did take me a couple of long feeling months to get to know people but I now feel I have a network of friends with children of similar age. There are certainly lots of things for little kids to do (mine are under 5). All the public swimming pools are free, for example.
There is also a ferry direct to central Auckland which takes half an hour.
It might be worth a look if you get offered any jobs in this area.