http://www.immigration.govt.nz/ I did this way back in 1998. Moved from Oklahoma to New Zealand. It's not too difficult to get a job here, and being American is a plus on that front. Downside is the cost of living (think Hawaii prices - everything costs more here than it does in the USA). The 'tyranny of distance' is the best and the worst thing at once. Upside is quality of life, and peace of mind. I've never regretted it.
Do it... I kinda miss not seeing the Big Dipper and other familiar constellations. Somewhat odd - in the North, you see Orion standing, or on his side, depending on time-of-year. In the South, he's either on his side, or upside-down (but it is one of the few easily-recognisable constellations you can see from either hemisphere).
Several aspects to this. From a personal perspective, the police presence is much less, and much less threatening. Our cop-on-the-beat does not carry a gun, and I think this makes a vast difference in the kind of person attracted to the profession. There's less abject poverty; we have poor people but the number of desperate poor is much less here - and that leads to less crime. We do have a lot of burglaries here, but other minor crimes seem much reduced. Also, a lot fewer handguns in circulation add to the general safety aspect. We have no dangerous animals to speak of as well. We don't have HFCS here at all (unless it's in US imports). We have better health care coverage and leave (full-time employees get 4 weeks minimum by law). Local dairy products, fruits and vegetables are great. Every tiny little place that serves coffee has an espresso machine and makes a great cup - it's hard to find places that serve old-fashioned 'filter coffee' any more. The weather is fantastic. The politicians aren't as corrupt. We have an MMP system for electing representatives that (in my opinion) is superior to yours (first-past-the-post), in that it allows smaller parties to wield real power. Kids here aren't afraid of strangers. I could go on (and I do!)
If you were to consider it, I would recommend sticking to the cities no further south than Christchurch. I live in the south, and there's noticeably less work around the place - so for a newcomer it might be a tad difficult. The main centres of Auckland and Wellington I imagine you would be absolutely sorted (although renting a house in Auckland is apparently becoming a nightmare!) And at the very least, I'll buy you both a beer upon arrival.