Hi Ben,
You will need a NZ license and if you fish the Taupo region it is a different license.
When you get the license you usually get the fishing regulations. This will tell you where you can spin, many South Island and North Island streams are Fly only.
When you get there the main holiday crowd will be back at work and hopefully the fish will not be so spooky. The big problem is the wind if you are only a modest caster and you get those winds off the mountains it can be a real challenge. So p[ractise asmuch as you can before you go.
I have fished the South Island around the time you are going and the weather is usually good. At present they have had a fairly dry summer but they did get some rain last week, so lets hope they get some more. Long leaders are usually needed (15-20') especially if the rivers are low and clear. John Kents book is worth picking up.
have a great trip.
Best regards
John