Hello,
This is one of my favourites!
Two years ago me and my family toured NZ over 7 weeks - 3 in the south and 4 in the north (2 were over Xmas + new year).
The ONLY way to do the south island in my opinion is by motorhome, unless you have lots more time. There is so much to see, you have to move on every day or two and if you had a car and had to look for accommodation in each town when you arrived, you would waste a lot of time. With a motorhome, you just arrive and plug in! Check www.top10.co.nz for the biggest campsite group in NZ. The majority of sites have very good facilities, and it costs about £10 a night to stay.
Hiring a motorhome is not cheap if you go during their summer (Dec/Jan), but like you say, it's transport and accommodation in one, and you eat cheaply to. Fuel is also very cheap. I think diesel was 20p a litre when we we there.
Auckland is huge and is the only real 'City' in New Zealand. One third of the population lives in and around it. Christchurch is very nice, but is more of a large town, whereas Auckland is reminiscent of Sydney in style and size.
The north island is different to the south, more volcanic than glacial scenery, and a stronger Maori cultural presence.
The most spiritual experience we had on our RTW trip was the guided tour of Waitangi, by a Maori warrior. Made the hairs stand up on the back of my neck.
Biggest surprise was to be told "Welcome Home" by Maoris.
