No one has really mentioned the south!
I am in the South Island. I've lived in Auckland and in London.
NZ gets less multi-cultural the further south you go and more sparsely populated.
I live in one of the major cities and I can grocery shop at any time of the day. Here, and in most places in NZ you are always pretty close to whatever you fancy as far as beaches, mountains, lakes etc. And there are lovely places that are not crowded or 'touristy'.
Because we are a smaller country (in terms of population and geography) I think that new technology and ideas are more easily adopted here. Our banking systems are very progressive (I've worked in banking) and we are just about cashless.
On the downside, I find my city to be very 'small' in terms of degrees of separation. Social circles are fairly small I think. (Maybe just mine?). And you can never go anywhere without bumping into someone you know.
When I moved back here after living London, I found it odd that people really stare at you on the street. In the UK, generally no-one pays you any attention. Here, everyone eyes each other up. And if you look a bit different, people really stare (in my city at least).
As a couple of others have mentioned, it is pretty difficult to get around without a car. The public transport system is nothing compared to the UK.
It's late here and I think this is a bit jumbled and rambly! Hope it makes sense. On the whole, if I was being really honest I would say that I wish I still lived in the UK. But don't let that put anyone off :)