I live in Wellington, NZ. I'm a kiwi, so can give you a pretty good idea of the cost of living in Wellington (which is in NZ dollars)
For 2 adults and 2 children, living in the central suburbs, you would need about $800 to $900 a week to live on. Rent is the biggest expense, as a three bedroom house in a suburb live Karori is about $350 a week. Food is also a big expense, and helps if you are a veg*n, as the cost of meat is high (due to most of it being exported overseas). We only buy organic, and it costs for 2 adults and one 11 month old child about $100 a week, but then it helps that we are vegans. Power is also another big expense, especially over winter if the place you are renting has minimal insulation and no heat pump. Over summer, our power bills are about $100 a month. Over winter, our highest was $450.
For phone and internet, go through TelstraClear. They have cable network for internet and pay tv. We pay $150 a month for digital TV, phone line, and cable broadband internet (which is 10MBps speed with a data allowance of 20GB a month).
For the trains, they have been a bit unreliable over the past couple of years. The bus is more reliable.
In terms of schools, there are no Reggio-style schools that I am aware of in Wellington. There is a couple of Rudolf Steiner schools in Wellington, with the main one is Lower Hutt (Raphael House) and a kindergarten in Thorndon. There are also a couple of Montessori schools in Wellington, but that go up to the age of 12.
Wellington is quite a liberal city, with all elected MPs in Wellington City from left-wing parties. There is a strong Green Party presence and support in place in Wellington (with the National HQ of the Green Party in Wellington). There are a couple of organic shops and a CSA also operating the Wellington region. Te Aro is quite a 'crunchy' suburb of Wellington. The city council has fantastic services for residents, with the library quite a popular place for families.
If you need any further info, just PM me