their summer is best, say February-April (Dec-Jan can be good too, but it's school holiday time and gets a bit crowded).
Get flights through Trailfinders.co.uk (other agents may be okay too).
I would also suggest more than two weeks if possible; it takes a few days to get over the jetlag.
Hiring a campervan is popular. Not the huge ones you get in the USA, but fine for two
http://www.maui-rentals.com/
Or hire a car and stay in motels. There are lots around. Most have kitchenettes so you can self-cater. You can get lists of hotels, motels etc from the AA (though it's no longer affiliated to the UK AA) plus maps. Or you can go on coach tours.
They'll probably fly into Auckland so from there it's relatively easy to get to the Bay of Islands (north) and the thermal/volcanic areas around Rotorua and Taupo (south), both well worth a visit. A bit off to the east is Napier, with the centre of town built mostly in Art Deco.
If you've got time to go further afield, Wellington (in good weather) is lively and has great views. Take a ferry from there to the South Island; you can visit winelands round Marlborough, whales off Kaikoura, the high country round the Southern Alps and adrenaline activity in Queenstown (which, apologies to Ratter jnr, is quite an expensive tourist spot but very beautiful).