Hey man, nearly everything he said was right.. but also very wrong. Just to clarify Auckland City center DOES NOT let you fly. The city has many helicopter operations and sea planes, therefore it is classed as being within 5km of an Aerodrome, if you fly in the city center and get caught you could get fined $10000. It has happened before.
Visit
www.airshare.co.nz they have a map of NZ with all the places you can’t fly in. You’ll find most of Auckland is actually in controlled airspace because of the Airport, this means you can only fly in a shielded operation (not to fly above the nearest tallest object (tree, building etc) within 100m).
Apart from that the other rules he said are pretty much right. Height limit and keep within LOS and don’t fly within 5km of an airport. A lot of the South Island has low flying zones which extend to the ground, so these to are a no go!