I am a young woman, and I backpacked in NZ alone for two months! I was able to afford it by participating in an organization called WWOOF, and another called Couchsurfing. Both are international communities, which help house (and in some cases feed) travelers. A wonderful way to experience a place, meet amazing people, and see things that tourists just dont get to.
I wrote a blog during my trip if you want to check it out…
http://landofnewzeal.blogspot.com/


