There were only 2 sites that supported IPv6, geekzone.co.nz and nzsale.com (although this is an Australian company). While there may be some smaller sites that support IPv6, I couldn't get a larger list.
This is really disappointing. APNIC was the first RIR to move onto their last /8 and have made it harder to get IPv4 addresses, so you would think that it would be incentive for site owners to enable IPv6. What's really disappointing is that most of the larger ISPs don't have IPv6 on their own websites (Orcon, Vodafone, Telecom, Maxnet, Slingshot). The only ones that I found were Snap and WXC.
I reached out to Trade Me who were working on IPv6 a while back, but have yet to implement anything. They have forwarded my email on to the tech team, but no reply yet. I also reached out to Web Drive (who claims to be the biggest host in NZ) to see if they have plans on implementing IPv6, once again I was forwarded on to the tech team, but no reply yet.
Come on NZ, sort it out. By this time next year there will be connections that are either IPv6 only or ISPs will be resorting to carrier grade NAT.