Well I'm going to be hopelessly biased and say Nelson. We always had a preference for the south island and it came down to a choice between here and Chch. Nelson won as part of our rationale for moving was to get away from living in and around a large city (we were from Essex originally). Chch has a lot going for it, but we felt we'd go the whole hog and go somewhere smaller. It's been great for the kids over the past seven years with safe, sandy beaches, lots of outdoorsy stuff, decent schools all close by and the area itself is pretty safe.
On the downside it can feel a long way from anywhere and the house prices are pretty 'robust' shall we say - not in Auckland's league though. I can't speak for Hawkes Bay, NP or Tauranga.
Wherever you decide to head for, nowhere need be permanent. Once here, there can be more of a freedom to be able to move to where the work is than I recall there being in the UK. The hardest thing will be the moving away from family and friends and support networks you may have. You'll need to make sure you can, and do, get your head around that aspect as that's probably the only thing you cannot readily recreate once you've moved over. It can be a tough ride at times - they say the first two years are the hardest - but if you can stick it out then I'm sure things will all work out well.
But for now, get the paperwork sorted for your visa and take things from there...
Let us all now how you get on. That's the good thing about this forum: you're not alone; you're not the first, and you won't be the last - you can learn from others and others can learn from you.