One thing you should definitely do while in New Zealand is rent a campervan to drive around! It was a highlight of our entire trip for me, and something I definitely want to do again.
We had just over six weeks to spend in New Zealand altogether, and we split it up into three weeks on each island: starting with the South Island. We chose to just do the campervan for the South Island (and a rental car for the North Island) as we had family to stay with in a couple places on the North Island.
We rented our campervan (we named her Beatrice) from Wilderness Motorhomes in Christchurch (they also have an office in Auckland on the North Island). We did a lot of research while back in Canada about which campervan was the best for us. We went back and forth about whether it would be better to get a slightly bigger van (for a lot more money), or one that's basically just a regular minivan converted into a camper (most of which don't come with a fridge - just a chilly bin/cooler). We went back and forth, and in the end we actually swapped the order of visiting NZ and Australia to get the much cheaper prices on campervans outside of peak season.
We almost booked with Spaceships before we found Wilderness. Wilderness was pretty much the same price, but a bigger van (a VW Transporter hitop-style cargo van instead of a Toyota Estima minivan) and a bigger fridge. They also had a motto/vision that more aligned with what we wanted: actively encouraging exploring your own way, freedom camping, taking dirt roads, etc.
While we did have a couple problems with it (a leaking water tank the first night which had us leaving it at a mechanic for five hours, and a blocked kitchen sink which had us having to drive an hour or so out of our way to get it fixed), we LOVED our Wilderness campervan. It had tons of space, lots of well thought out storage, a bigger fridge than we were expecting, and an easy to put down bed. The van was also surprisingly easy to drive, and it wasn't too big to ever have an issue parking anywhere.
We had everything there with us at all times: stove, fridge, food, bed, even a portapotty if we needed it (this allowed us to be classified as "certified self contained", which meant we could camp in places that regular cars without a bathroom and adequate water supply couldn't). We could nap in a parking lot in the middle of the day, or cook dinner one place then drive down the road to camp somewhere else. It was so great to be able to just stop and cook whenever we wanted. We cooked all our meals, a welcome change after months of eating out in Asia, and found it well equipped for all sorts of meals.
Of course there were a few chores to be done - emptying the grey water, filling the fresh water, etc.
But then you have times like this to savor.
Before we left, we downloaded an app called Campermate (it's free!), which definitely came in handy. It can be used offline, which was awesome as we didn't have much data on our phone. There's a map with all the facilities you could possibly need: campsites (both free and paid), bathrooms, internet, grocery stores, restaurants, etc. You can turn each category on and off to only see what you're looking for on the map. We found basically all of our campsites on here, as well as bathrooms and where to find wifi.
New Zealand is cutting down on their "freedom camping", with many local councils adding bylaws to restrict camping to certain areas, and fines for any kind of infraction are $200. Still, we found there are a lot of places you can still camp for free, and most even had flush toilets still. We stayed every third night or so at a Holiday Park, where we could recharge the power on the campervan, charge up all our devices, and shower. The other nights were spent either at a free, or cheap ($5-10 each) DOC spot. We came across so many beautiful spots to camp!
There wasn't too much traffic on the South Island, I think in part because it's a lot less populated than the North Island. Most of the traffic we did see were campervans like us! We did have to stop a few times for these guys though...