Hi there YoungSteelheader
I'm a trout fisherman in New Zealand (Hamilton, Waikato, North Island) and would be happy to help you out with a few tips if you still need it.
The fly rod size depends on where you will be fishing, what size/weight flies, and the size of fish likely to be encountered.
For example, I use:
#5 rod for dry fly & light nymphs on small streams/ small fish.
#6/7 rod for med/heavier weighted nymphs on larger streams
#8/9 rod for really heavy bombs and nymphs, or wetlining / windy weather, on large rivers and lakes. (ie Winter Rainbow runs in the Tongariro etc)
If you are here over Feb / March its a great time to cast a dry fly to sighted fish. They can be fussy though, so it pays to have a good selection of flies. Trout are taking Cicadas right now, however I have had a few small local fish reject them - and take a small Mayfly imitation instead.
The river mouths flowing into the Rotorua and Taupo Lakes are also a good spot at this time of the year. As the lake water temperatures increase, large schools of trout congregate in the cooler water at the mouths - so the fishing can be fantastic.
I landed my best ever fish (10 pound Brown)on a smelt pattern at one of these locations.
Here are a few more websites for you to check out:
http://www.fishing.net.nz/asp_forums/
http://nzfishing.com/
http://www.sportinglife-turangi.co.nz/pages/fishing.htm
Let me know if you have any more questions, could also make contact when you are over here if that helps.
I will be travelling through Canada (BC & Yukon) and Alaska from April to July this year, so will also be keen to learn a bit about your local fishing. I'm really looking forward to trying out some Salmon fishing.
So where will you be fishing while you are in NZ?