I have done a little research and found out that McDonald's like here at home has free WiFi and so does Starbucks and most BP petrol/gas stations (purchase necessary).
Here is a google map of NZ free WiFi spots
McDonald’s claims it is now the largest free internet provider in New Zealand.
Today the company announced that it is offering free wi-fi in nearly all its restaurants nationwide.
TelstraClear is the service provider.
There is no time-limit, but here is a data limit of 50MB per customer.
McDonald’s free wi-fi is currently available in 132 restaurants nationwide from today, with 145 restaurants expected to be offering the service by the end of the year.
Here is a wiki list of free WiFi spots
Not sure if these are free, but some may be and some may not
Remember that public libraries in New Zealand also have free WiFi service.
Fans heading to Wellington, New Zealand for the Rugby World Cup will find free Wi-Fi service in many parts of the city.Christchurch will have free WiFi until the End of October...
Among the areas of coverage are Waitangi Park and Courtenay Place all the way to the Westpac Stadium and up Cuba Street, the Zoo, Zealandia, the Cable Car and Carter Observatory.
Telecom's free WiFi for Christchurch gets the thumbs upHere is another list of free WiFi Hotspots
Telecom has installed more than 50 free WiFi hotspots across Christchurch so residents can access the internet for free as the city recovers.
Telecom's new WiFi hotspots will allow residents to access mobile data, email and the internet, free of charge, providing they are within range until the end of October.
Lastly, this is a list of WiFi spots, likely not all free!, I thought I would still include it as a resource.