I have not worked in the New Zealand market, so I can not speak specifically to that context, but I will include a few notes on the core principle that you are attempting to overcome -- Localization.
Aspects of localization include technical aspects of the local market, making the product behave appropriately in the national market, and addressing specific cultural values and conventions.
I can speak a little to the technical aspect, specific to New Zealand -- observing the following during a 1-month trip to NZ a few years ago. Internet is NZ is not as prolific as it is in the US, and WiFi is almost never free. Every city has at least one Internet cafe, and they always have people in them. Unlike the US, where Internet cafes died out before most people knew what they were, they are an important part of the NZ Internet infrastructure.
That means people have intent. Unless you're at home (in NZ) you are almost certainly paying more for the ability to log onto the Internet. If you're a tourist (like we were) you are absolutely paying for Internet. That gave us intent! When you're paying by the minute you want to get in and get our as quickly as possible.
Depending on the customer target for your product site, a more focused experience may be preferred. When we needed to log on in NZ we thought about our plan of action first. There was no clicking around for clicking's sake.
To more general points of consideration when working to localize to a particular market:
Do images and slogans used work in each country? Many marketing translation mistakes have resulted from this.
Colors are very important. Red is often associated with more angry/negative feelings in the USA, but is seen as good luck in China.
Users find different things acceptable in terms of cultural variances and expectations. Different cultures may have differences in how they execute tasks, altering your task design. Similarly, does navigation structure work across cultures?
While not as specific to this case, language and reading direction should be considered when dealing with an overall localization. Actually, perhaps your client might want to expand into a global market -- making this very important!
Lots of little details...
- Dates are commonly MM/DD/YYYY in the US; DD/MM/YYYY in NZ
- Imperial vs metric systems
- Monetary format
- Time formats
Engaging with the NZ client and asking the appropriate questions on how to best cater to their customer base could be to your advantage. They know you're not local, but you're asking the right questions to give them the best product but focusing your attention on their users (instead of the users you normally deal with).