I am in Wellington, came 3/4 years ago with kids then aged 8,5,2. I absolutely love it.
Your motivations are similar to the ones we had, and they have been exceeded: we live in an amazing house which cost the equivalent of a 3-bed terrace in Zone 5, the children have a fantastic lifestyle, with an education system which is not pressured, and which is far more about producing rounded individuals.
Springstonchick is spot on with costs and availability of goods and the things we missed in the first month we still miss now (decent media, M&S, Waitrose, selection of clothing and household items). Some costs are eye watering such as our weekly supermarket shop, but others substantially lower: mortgage, childcare, car / transport.
Over time we have also realised that it's really, really expensive to leave the country, not just to visit UK, but also for mid-level family holidays, you can't just zip off for a cheap week in Greece or France. We therefore haven't travelled as a family as much as we'd have liked.
Another negative not much discussed is that whilst housing (outside of Auckland) is much cheaper than the UK, the build quality is generally dreadful, so houses are often really insubstantial, and built to poor building standards in terms of insulation, electrics etc.
You can look up stats for median incomes in NZ, but my feel is that a household income of $100-150k would give you a comfortable lifestyle. The job market in Welly is quite limited, so good that you're checking out already.
On re-read that all sounds a bit negative! We have a fantastic lifestyle here, interesting jobs, kids who are growing up with the beach on one side and the bush on the other, a great set of friends who made us feel part of a community very quickly.
Do it!