I did a bike tour in NZ in 2007, it's a stunning place, I wish I could go back. Generally there will be a lot of light, the 28-105WR is a great choice. A 14mm would be good for some of the wide views. A tripod is a good call but honestly I didn't need one for most of the time I was there. There are a lot of tourists most places, you have to worry about the tripod being in the way, etc.
I'd say 28-105, 14, maybe the macro.
How many days will you be there, which Island?
Important gear -> HIKING SHOES and a rain jacket. There are so many good hiking opportunities, some short, some long. Bring thee hiking shoes.
People are friendly there, if you are friendly and talkative you might just find some cool sights off the beaten track. The tourist industry is huge and varied, but you don't need to spend $$$ for most of the sights.
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There's lots of funny stuff built, probably back in the early 1900s. It's a quirky place, keep your eyes open and you never know what you might see... :^D
Make sure to go to the Kauri museum if possible!