Maria
We toured New Zealand in February this year and although avid caravanners, when I did the research I found it was cheaper to hire a car and stay in motels. This was especially so when I found that most motels have very good kitchen facilities so are as flexible as a motorhome when it comes to eating. Also, if you are traveling round both islands (allow at least 2000 miles) a motorhome is slower and more bulky to drive on the generally narrower roads - although trafic is very light and fuel is cheap.
One thing to remember when hiring a car or motorhome is that there is a very big market catering for backpackers and people on a tight travelling budget. To keep costs down for these customers many of the cheaper vehicles hired out are old and can be very basic. This is great if you are a student or on a tight budget, but if you are older (like me!), like a bit of comfort and are willing to pay more for it you are better off avoiding the cheaper companies and going for the more upmarket ones, which are easily identifiable if you study their web sites. There are many companies who do hotel/motel bookings and car/motorhome rental - just look up Car Hire New Zealand or Hotels New Zealand on Google. You can even stay in cabins on campsites, but we tried a few and found they were not as comfortable as motels.
A good way to do research is to go on the "Trip Advisor" forums for NZ, where you can talk to locals and other travellers.
All in all touring New Zealand was a wonderful experience, there is a great variety of scenery, it's much less crowded almost everywhere, and prices are generally low compared to Europe.
Hope this helps. Don't hesitate to ask if you have any specific questions
Keith