Upvote:2
How sensitive to cold are you ? How fashionably conscious are you ?
I suggest bringing at least one good rainwear and one good sweater and some good water resistant walking shoes (or boots)
A quick search says that Auckland NZ temperature vary from 10C-20C (1) and a little bit warmer in Sidney (Aus), but that can vary a lot if going to different areas of both New Zealand or Australia (Darwin, for example is hot).
(1) http://www.accuweather.com/en/nz/auckland/252066/june-weather/252066