I spent 10 weeks touring NZ and didn't see it all and did some 6000km trying. Four weeks is not enough.
Brilliant cycling. There's a community of cyclists touring and they often go the same way. So you meet someone, ride with them a day. Then you go one way and they the other and then a week later meet them again. I met two Germans who were cycling togther early in my trip (who happened to meet). They gave me some gossip about a couple of cyclists one Swiss and one Irish who had met and fallen in love and were now travelling together. 8 weeks later on a dirt back road near Queenstown, I stopped to chat to two cyclists coming the opposite way. The two of the gossip.
As for the people they are dead friendly and helpful. The two Germans above had been trusted with a key to some guy's summer house to which they, and then me, were headed. Had another guy stop as I was oiling my chain to check I was OK. I was a little embarrased to have made him stop.
I met a whole Iwi (tribe) of Maori on the Bay of Plenty. I asked mirely to sleep under the awning of a community club and got invited to their Xmas Party at their Whare Kai (eating house). I met my invitors and all their relatives and their relative's relatives. Marvellous! I spent two nights in the Iwi's Whare Nui (meeting house). After the party I woke the next day surrounded by Mauri. One older guy next to me said "I never thought I'd wake up next to a white guy" and we both laughed our heads off. I spent a day being taken round by a guy called Robert Maxwell who explained many Mauri traditions to me. When I left on the second day it took me 6 hours to write up the experience and traditions i my journal.
I rough camped everywhere, except where I had a personal contact. Mostly personal in the sense that I didn't know the person before I met them. I stayed with a family in Wellington I had never met. One of my best friends at the time had and Aussie girlfriend. She told her friend who was from NZ, who told the girlfriend to tell my friend to visit. Two days out on Wellington I rang to give notice. I spoke to the NZ girl's mum. I explained how I "knew" her daughter to be told that she wasn't there but back in the UK. The Mum asked me to explain it all again (my mate has a girlfriend I have never met who knows your daughter who I have never met. Mum says "Oh come along anyway, that's how it works in NZ." And it is how it works in NZ.
Robert Maxwell gave me a brother's address in Christchurch and told me to call in. When I got to Christchurch it was a couple of days before Xmas - not the best of times to be asking to stay at someone's house. I rang. I spoke to his wife, she said "oh, such a shame as we are going away for Xmas, but Robert has another brother here and this is his phone number...."
I could give you more stories of being given addresses of people who then gave me addresses of other people who.... Wonderful, amazing
The only problem was the rain. I had one pair of shoes that never really dried out the first 8 weeks of my trip. In Gibson, I re-met one of the Germans mentioned above and we agreed to meet the next day to spend a day or so cycling together. The next day was wet and I said to the guy, "You don't have to go just because we agreed to go". He replied, "If I don't go today it will make no difference. It will be raining tomorrow." And off we went together. Luckily on the North Island it's warm enough to cycle in the rain. But the South Island colder and especially anywhere in Invarcargill is miserably cold. (I and another cyclist turned north here [you have to but if you didn't you would want to.] As the other said "I'm on holiday, why be cold?")
Strangely enough the driest part of my trip was the West coast of the South Island (the wettest part of NZ). By the way do this section south to north and you get a tail wind.
You must do the North Island first as it's beautiful. Then do the South Island as it is more again by far and away.