Campervan is the way to go, we drove around the South Island for 4 weeks last September and mainly used the DOC (Department of Conservation) campgrounds, I think we paid around $12 -15 for the van and us three and mostly had the places to ourselves. But make sure to take warm clothing, we stepped out into snow one morning at Mt Cook – loved it !
I didn't find it more expensive than here, maybe for some items but then others were cheaper than in Australia.
We totally enjoyed the family experience with our 11yo, being 'stuck' in the campervan of a night, no TV and electronic toys but campfires, walks, games and reading instead, wonderful.
And the landscape is that stunningly beautiful (plus we were extremely lucky weatherwise, only had 2 days of rain on the West coast), I could have stayed. In fact, we're still thinking we might move one day, just not sure what on earth people do for work...