Några NZ tips från min sambo som är kiwi. Han har bott och rest i stora delar av landet, dock är hans svenska inte flytande ännu så hoppas att det går bra med engelska..
North Island
Out on the west coast is very beautiful, my favourite sunsets in the world also. There's Piha, with black sand, a bunch of walks, Kite Kite falls is really nice for a short walk and there's plenty of longer ones there also, there's an info center on the way out there. A little further north is a Gannet colony, if you want wild life, some dude got eaten by a shark there recently though so wouldn't go swimming there.
You can also take dolphin and whale tours right there from downtown Auckland which is nice.
Coromandel
A few hours drive from Auckland is the coromandel peninsula, it's really nice, all the tourists go to cathedral cove and hot water beach,
Rotorua
A lot of tourists go here also, there's some world class mountain biking and a lot of maori culture. It's geothermic, so smells! But there's lots of cool things like mud pools etc. The camp ground in the city is pretty cool, if you're in a tent the ground is warm so nice and cosy, free natural hot pools and a 'hangi' pit for cooking food.
Taupo/central plateau
Near Taupo there's a one day hike over some volcanoes, it's all the tongarrio crossing and it's very beautiful, we did about a year ago and it was amazing. The main volcano is mount doom from the lord of the rings! You would need to check the snow levels etc first, not sure how it will be this time of year.
On the side of Taupo is one of the 'great walks', lake waikaremoana, you need to book the huts and I think it's about 4 days. Jennie and I are planning to do it when we're back in NZ this summer. Here's a bit more info on the great walks, you probably want to get one in at least, apparently Milford track is suppose to be the best (that takes us to the south island), DoC is the organisation that looks after these things:
Great Walks: Tracks and walks
South Island
Able Tasman
It's really beautiful here, the top of the south island. There's one of the great walks here, along the water front which would be nice. I did it a few years ago by kayak which was amazing. Highly recommended.
St Arnuad is nearby which is a great spot to get into the mountains, you can do an easy walk around the lake (overnight) and if you want continue into the mountains, this area is pretty rugged and much less 'groomed' than the great walks. After, if you head towards christchurch there is Lewis pass, and Hanmer which are both great spots.
Bank's peninsula
This is just out of Christchurch, Akaroa is nice but the great thing there is you can go swimming with the hectors dolphins, they're mini dolphins! I really enjoyed that.
Arthur's pass
On the way from Christchurch to the west coast is Arthur's pass. Be sure to stop at castle hill on the way, amazing rock formations there. There is some caving around there which is pretty easy also. Arthur's pass has a LOT of hiking, I spent four years around the area every weekend, doing something different each time. It's pretty full on tramping around there though, but if you just pass through be sure to check out the devils punch bowl fall, over 100m high or something and just a 15 min walk or so. Try to find the Kea's, the world's only mountain parrot, amazing and super cheeky.
West coast
It's a pretty amazing drive from Wanaka to the west coast or the other way around, but on the west coast are the glaciers which are of course worth checking out, I took a helicopter ride last time. The Pancake rocks are cool also and worth a stop.
Wanaka/Queenstown
Fairly touristic but you can get your bungy jumping and other adrenaline thrills here. My favourite thing to do is take the gondola up the hill, great view, cool luge and pretty much the cheapest thing to do in town. Ferg burger is supposedly a must try also.
Fiordland
To me this is the most beautiful part of NZ, it's a long drive though from Queenstown but totally worth it. The milford sound is great and is suppose to be the best of the 'great walks' but is far south.
There is a bit of petty crime about, especially car brake-ins, so don't leave valuables etc insight especially if you leave your car somewhere. And remember 'right side is suicide', keep left when driving!
Have a great trip!