I grew up there, in Auckland, now I live in London.
In a way it's a quiet place compared to the UK, like there's not much going on in the news, there are far fewer people, smaller cities, etc. But in other ways it can be very lively - the clubbing scene in Auckland is (or was at least) anything but quiet, plus theres a lot of sports and extreme sports going on.
Apart from a slightly different culture, you will find Auckland to be just like any EU or US city, only smaller. The main reason tourists go there is the outdoors - the beaches, rivers, mountains, forests are some of the cleanest and most unspoiled in the world. There are some great romantic spots (thinking honeymoon stuff here) like theres this place in Taupo where hot springs run through a series of rock pools into the cold river and form little natural hot tubs of different temperatures. Anywhere else in the world stuff like that would be turned into a 'health spa' or at least crowded with people, but not in NZ. Same with the beaches - with not too much effort you can find a perfect beach where you're the only people there.