It has been 15 years since my last trip to NZ. I was primarily on the South Island. I did not go into any dedicated quilt shops, but did enjoy a trip to Spotlight in Dunedin and a lovely fabric store there too. I do not remember the name of the fabric store.
Fabric tends to be quite $$$, as it all has to be imported great distances.
You could ask Gourmet Quilter
https://www.gourmetquilter.com/ for recommendations.