OK, going up from the north, down to the south.

Stewart Island:
**It is a tiny island underneath the south island
no barely anything about it so see:http://www.stewart-island.nz.com/activities.aspx

Invercargill:
I haven’t been there so i dont really know if there is much to do. Famous for oysters tho
http://no1guide.co.nz/destination/invercargill/top-11-things-to-do-in-invercargill-751.html

Wanaka:
Famous for its skiiing/snowboarding mountain place

Christchurch:
Plenty of beautiful views
see:http://www.christchurch.org.nz/Activities/

Wellington -capital city:
The Parliamentary building – The Beehive
Te Papa – A well known museum, tho I haven’t been there i’ve heard A LOT about it, it has a lot of stuff about native new zealand stuff, good for tourists.
also see:http://www.ki-wi.co.nz/wellington_activities.htm

Taupo:
Huka falls
horse riding treks
helicopter rides
Fishing charters;always catch a fish! (trout/rainbow trout)
Mt ruapehu, nz’s popular mountain for skiing and snowboarding. see:http://resor.smedendahl.se/nzpics/089-NZ-Mt_Ruapehu.JPG

Rotorua:
Lots of thermal places you can visit and see
Luge
There’s plenty of other things to do, i’ve been there and there’s lots of touristy places.
Also see: http://www.rotorua.nz.com/activities.aspx

Goat Island:
Snorkelling mainly
http://www.goatislanddive.co.nz/Accommodation___Area/Matakana_Coast_IDL=1_IDT=321_ID=1708_.html

Auckland:
Luge
Auckland museum
Botanical gardens
Snowplanet – Indoor snowboarding, skiing and tobbogganing place!
Auckalnd Zoo
Sky Tower
K-Road
Aslo check out this site:http://www.aucklandnz.com/index.php/listing_A/?L1=63&L2=76

*you can also do skydiving in various places in NZ, check google for that.
References :
I live in New Zealand, Auckland, & have lived here for 11 years.
Hope I helped! Have a great time here.

QUEENSTOWN/SOUTHERN LAKES

Milford sound/fiordland
Skippers canyon
Arrowtown
Shotover jet
Kingston flyer (train)
AJ hackett bungy
Queenstowm gondala
Coronet Peak (skiing and snow boarding)
Glow worm caves

CANTERBURY

Dophin swimming
Banks Peninsula track
Hamner Springs (town)
Fishing
Whale watching
Dolphin swimming or watching and bird wathcing
Seal swimming
Maori Tours
Wildlife tours (blue penguins, Northern Royal Albatross, seals, seal lions)
Taieri gorge railway (one of the worlds greatest train trips)
Southern Alps
Anatarctic centre
Wildlife (rare birds, and the kiwi)
Gondala
Southern Encounter Aquarium & Kiwi House
The tasman glacier ( biggest galcier in nz)
Mt Cook and southern alphs

WEST COAST

Crystal clear lakes
Southern Alphs
Glaciers
Wildlife (rare birds, glow worms)
Subtropical rain forests
TranzAlpine train (one of the worlds greatest train journeys)
Gold panning

NELSON & MARLBOROUGH

Abel tasman
Wine trails
Skywire flying-fox (longest in the world and can go up to 100km)
Marlborough sounds
Dolphin watching
Buller gorge swingbridge
Seal swim
The piction ferry (going to wellington through the marborugh sounds and cook

straight)

WELLINGTON

Lord of the rings locations
Te papa (museum)
The beehive
Cable car / botanical gardens
Kaori Sanctuary
Helipro (helicopter over wellington, marbourough sounds, abel tasman,

kaikoura, whales and dolphins)
Interislander ferry
Wellington zoo

HAWKES BAY

Gannet beach

ROTORUA

Maori tours
Thermals
Mud pools, Geysers
Volcanic valleys/Goethermals
Crystal clear lakes

TAUPO

Lake taupo
Taupo Bungey
Huka falls
Taupo museum
Terraces, Geysers
Maori carvings and people etc…
Mount Ruapahu (skiing and snow boarding)

GISBOURNE

Tangaroa – shark cage diving and sting rays, seals, and dolphins.

BAY OF PLENTY

Whale and dolphin watching and swimming
White island

HAMILTON/WAITOMO

Hamilton zoo
Waitomo caves
Kiwi house and native bird park

AUCKLAND

Whale wacthing
Auckland zoo
Rainbows end theme park
Auckland harbour bridge
Sky tower
Luge
Kelly Tarltons
Sail on a americas cup yahct (even help drive it)
Auckland bungy

NORTHLAND

Cape Reinga
Ninety Mile Beach
Kite surfing, diving, fishing, kayaking, wakeboarding, swimming with dolphins, snorkeling, surfing, stand-up-paddle boarding.

And pretty much throughout the whole of New Zealand there is:

Water jets
Cruises and boat charters
Helicopters
Small planes
Horse trekking
4WD
Quad biking

Too see the main sites and best out of site scenary.
References :