you said youll be studying in auckland right?
you can rent an apartment by youself for about NZD$250-300 a week! or share accommodation thru ads in the paper for about $70-$100 week in or walking distance to the city.
it also depends on if you want to have a car or public transport.
look online at the nzhearld. i think its url is www.nzherald.co
. but its only for auckland (strangely) every thursday i think it is they update their accommodation coloums.
hope that helps