Hi,
I've been a couple of times, it is a beautiful country for a driving holiday. I would stick with a small manual car and staying at hotels/motels rather than a camper van. The campers are good once you are out of the built up towns, but they aren't the best when you are driving in the built up areas. But that's a personal choice. There are plenty of accommodation spots that are generally inexpensive. I don't tend to book ahead, unless there is an event on that is popular.
With regards to timing, you will need at least 2 weeks to see both islands, and you will only get a glimpse of them in that time. Ideally you would have 4 weeks. In the north island, Auckland is the biggest city and is similar to Sydney or San Fransicso being built on a harbour. It is pretty enough, but I preferred getting out and heading north up to the Bay of Islands for better ocean scenery and relaxation. Make sure you get to Rotorua in the centre of the north island, it has geysers and boiling mud pools and is great to see. The smell is sometimes arresting though, but you just grin and bear it, the scenery is worth the smell. Wellington is the capital at the southern tip of the north island. It is definitely worth stopping for a couple of days, great eateries. coffee shops and bars. You can get the car ferry over to the south island from Wellington.
Picton is the other end of the car ferry trip to the south island. It is not that far, the journey should take a couple of hours. Picton is a small coastal town, not that much to see, but if you like fishing or cruising, it is a good base for a day trip to the Queen Charlotte sounds area. There are also some great walks to take in this region of the south island. Heading south will take you into the Marlborough wine region and if you like Sav Blanc, you will be in paradise about now. There are dozens of wineries to visit if that takes your fancy. Heading further south along the east coast will take you to Kaikoura which is good for dolphin and whale watching cruises. You can also see seals along the coast at just about any spot where the rocks poke out of the see near the coast.
Before you get into Christchurch head inland to visit Hamner Springs. This place has some great heated pools which are fed by natural hot spring water. Plan on spending a day here and definitely got the the springs and have a swim. You can go from hot 30 degree pools into cold 10 degree polls and back again all day. It is invigorating. Heading further south will take you into Christchurch. ChCh is lovely, but it has been hit hard by the earthquake in 2011, so some of the beautiful blue stone buildings are now gone. It is still worth a visit though and I'd suggest 2 days.
Heading further south I'd take the inland road heading towards Wanaka. Along the way you can stop in at Fairlie bakehouse and get a lamb and mint pie (best pie I've ever had) and wash it down with a Speights lager. Take some time to go for a walk (it's called tramping in NZ) up to the base of Mount Cook which is the highest mountain in NZ. The walk to the base is beautiful and if you are lucky, the summit will be free of cloud cover and you will get some of the best photos you are likely to take on your trip. Heading further south will take you to Wanaka and then to Queenstown. Queenstown is breathtaking, but it is expensive compared to other places in NZ. I'd recommend staying in Arrowtown (just outside of Queenstown) and just visiting Queenstown for day trips. Allow at least 2-3 days in this area, there is plenty to keep you occupied. The jet boat trip was my highlight, but the luge runs were a close second followed by the flying swing.
After this, if you still have time available, head south to Milford Sound and Doubtful Sound. These sounds involve a long day drive from Queenstown, but the gorges at the end are beautiful. Both gorges feature near vertical rock faces down into the water. Milford is a 2-3 hour cruise which take you out to the ocean mouth where you can see dolphin and seals on the rocks, plus all the waterfalls along the way. Doubtful takes you over to the power station where you can get inside and see how the power station operates. I enjoyed both.
All in all, NZ will leave you wanting to go back, because you will only see a fraction of what is available.
Enjoy,
Brad.