hey hey!
if you are coming at end of december, i suggest flying into sydney, but if you are wanting to do nz, maybe at the start, and be one of the very first countries to celebrate new years, or if in aus, sydney. melbourne around xmas/new years can still be pissing with rain, as could syd, but not as much.

things to do/see:
harbour bridge/opera house (sydney)
blue mountains (nsw)
bondi beach (sydney, will be very crowded in summer, but you may get to be on tv)
newton/enmore (sydney)
the rocks (sydney)
rialto towers (melb)
st kilda beach (melb)
most of melbourne cbd lots of little laneways hiding around to explore
dandenongs (vic)
phillip island penguins (vic)
you can also go ice skating in summer in melb for something different
theme parks (qld)
surfers paradise (qld)
great barrier reef (qld)

a few ideas…….

havent really done the tourist thing in aus, cept for sydney and qld home town is melbourne.