Can't think of a better way to see the best little country in the world than by bike!

Some things to bear in mind:
* There are lots of hills.
* Some (okay, many) of the roads you would ride on aren't particularly smoothly surfaced.
* There are areas where it is a long way between towns with places to stay.
* There are a lot of areas where drivers aren't going to expect to see cyclists.
* Good public transport is not prevalent.

None of these have to be problems, but they are things you need to take into account when training and planning. I can't think of any bike touring companies off the top of my head (although they will exist!), but I do know there is a Lonely Planet Guide for cycling in NZ.

It won't be cold late in the year (Nov/Dec), but your chances of getting rained on are higher around then. Summer is Jan/Feb; it can get pretty sweltering in some parts of the country. March would be a really good time to come, weather wise - settled and not too hot.

There's a few Kiwis around here, so by all means, ask away if you have any more specific questions.