I think the bug is 'didymo' (sp?) or something? They're paranoid about it getting between Aust & NZ. If only they'd been so vigilant about Russell Crowe.
They check boots, tents (especially the pegs), walking poles etc for traces of soil. So it's a good idea to have those things on top of your bag, inside, to make it easier to get at.
Christchurch has a good range of climbing gear - yes, even chalk! - but it is significantly more expensive than the US and the range more limited. You might find, with the exchange rate, that some soft goods - fleece clothing etc - is OK value in NZ, so don't go overboard bringing that stuff.
Know that though your luggage allowance US-NZ is 2 x pieces of 32kg = 64kg (or 2x23kg=46kg) the allowance on separate
internal domestic flights (Chch-Dunedin) or flights to Aust is only 20kg.
The currency exchange desks at the airport give the same rate as the banks in town. There are ATMs everywhere, otherwise.
I've found the buses expensive and slow, so I usually hire a car. If you book in advance, http://www.standbycars.co.nz/
is usually the cheapest by far.