getting a tourist visa from the south island

I am living in Wanaka on the south island for the winter season. I will be traveling to China in october to visit my parents who are living there at the moment for work. I am an american citizen but won't be making it to Auckland before i'm scheduled to fly out. Is it true I cannot mail in my passport and visa application? if so, how do i go about getting it the embassy to get it all taken care of?

Thank you