Try the
NZ Herald classifieds or
www.flathunt.co.nz or
www.flatfinder.co.nz OR go to
www.crockers.co.nz. We rent our place through Crockers and they are very good.
You probably won't find anything in the central areas for the price you are looking at if you want a 2 bedroom.
West Auckland and Albany (North Shore) perhaps would be your best bet probably.
Good luck!