This entry is a continuation of my Transport entries, which have described air, bus, ferry, and train travel within New Zealand. This last entry describes modes of transport which give you much more freedom, namely having your own car or bike.
Renting a car in New Zealand, just like in any other part of the world, is expensive. However, if you need the flexibility that only a car offers and you don't have enough time in the country to justify buying a car, this quickly becomes your only option. I found that while some companies do offer rates as low as $25/day, you often won't be eligible for these special deals, since they are for rentals on the second Sunday after the first full moon of the apocalypse or some other rather odd time period. When I looked for a week-long rental to pick up in Queenstown and drop off in Christchurch, the lowest rate I could find was $50/day for a manual (without the insurance fees!). Granted, this was around Easter so it was quite busy, but you will end up paying a lot for the convenience of a car no matter what time of year it is. To top it all off, petrol prices aren't exactly low in NZ--they were significantly more than those in the US and I'm sure they have continued skyrocketing since I left.
The most popular rentals in New Zealand are campervans, which are beds & kitchens on wheels. Campervans are everywhere in NZ, and they are very noticeable given that many of them are painted with all sorts of obscene slogans. Campervan rental is quite expensive as well, but if there's two of you who plan on sleeping on the bed in the back in campgrounds it saves you quite a lot of money on accommodation. The main downside to having a campervan is that you don't get the hostel experience; it just seems a lot more insulated.
One important aspect of renting a car is the need to make sure you are aware of the driving conditions in NZ before you get behind the wheel. First of all, roads in New Zealand are not great--while they are kept up for the most part, many are windy and dangerous if you do not take proper precautions. In more remote areas, you'll have gravel roads and fords, so you should look into the conditions of renting and make sure what the company will and will not allow you to drive on. Also, the national speed limit is 100 km/h (60 mph), and there are plenty of cops around that can and will nab you as soon as you inch over that limit, and the fines quickly add up! I talked to at least three people that had never had a traffic infraction before in their life and had racked up multiple ones in their time in NZ.
As I was never able to rent a car or campervan, I cannot give more detailed information than that, but there are a few sites that can help.
Escape Campervans (these are the ones that are always brightly painted)
Ezy Car Rentals
Buying a Car
Many of the people that I met in New Zealand had bought their own cars, since they were going to be in New Zealand for a period of time that made renting a car infeasible. These cars were bought through backpacker classifieds or simply just ads that were posted on message boards in hostels. There are loads of cars being offered from $500 and up, depending on the quality and size of the vehicle. Most of the cars have a huge number of miles clocked up on them because they've been on the backpacker circuit for years, but there are definitely some quality vehicles out there--you just have to take the time to look for them. I'd say that if you're planning to look for a car in a city like Auckland or Christchuch that you should plan on being there for at least two weeks so you can scope out the ads and get a good inspection done on any prospective car before buying.
Along with buying the car and petrol, you will also have to register it (although some of the cars on sale have been registered for 6 or more months after the sale date) and get insurance. This isn't something I can help with, however, as I never intended to buy a car.
Other concerns to do with having your own car (in addition to those already detailed in the rental car section) are parking and transportation between the islands. Some hostels do not have abundant parking, especially those close to the centre of cities like Queenstown. It was miserable trying to find a car park at Deco Backpackers, and once we found a park we left the car there for three days just because we didn't want to go through the hassle again! Also, if you are going to be going between the north and south islands, you need to consider the price of the ferry crossing--at least $190 for just one person and a car.
A few good resources to start your car hunt are the Backpacker Board noticeboards and the BBH noticeboards. Each individual hostel will normally have its own noticeboards as well.
I met a few hardy souls that peddled their way around the entirety of New Zealand. They bought bikes and trailers upon arriving in the country and then travelled up to 150kms a day across the very-not-flat terrain of the country. I did not envy them at all, especially the British backpacker that had to pack his bags and cycle in a downpour out of Murchison! Like hiking, biking would definitely teach you the value of every vista you see and you'd appreciate the landscape a lot more after having to madly peddle uphill with your life in a trailer constantly trying to pull you backwards...but I couldn't have done it. I feel like I would have spent all of my time either on the bike or sleeping once I arrived at my destination, rather than enjoying my time there. However, there are clearly people that enjoy this because we were constantly passing bikers on the highway!
I recommend checking out the noticeboards that I posted in the "buying a car" section if you're looking for a bike. If you're looking for a new bike, I can't offer much help, but there are quite a few bike shops in all of the major cities in NZ.