Luckily I have three weeks planned :) But I'm curious to know what everyone would do if they only had one day in New Zealand?

It totally depends on your interests, fitness level etc. I would do something at Aoraki-Mt cook, such as tramp up to Sealey tarns & Mueller Hut.

Walk along the lake from Queenstown to Frankton and/or drive from Queenstown to Glenorchy, the heart of the Middle Earth.
I can spend a whole month enjoying the beauty within 200km of Queenstown.
https://www.flickr.com/photos/youngadventure/albums/72157656359104501
Great question!
Mt Cook! No, wait... Lake Tekapo. Errr..... wait, Rob Roy area hiking up and over to Queenstown side. Errr... Routeburn! Wait... Milford sound...
Have a great trip!
I would walk to to the local museum to see what the what is important to the locals. Then walk to the botanical gardens to see what native plants look like there. I would eat in a small, mid range cafe/restaurant.