Must-see

There are a number of things to do or to visit in NZ.

Things to do or visit Done?
Marlborough Sound
It is rated one of the most beautiful places even amongst Kiwis!
Giant Kauri forest
These giant trees are up to 2,500 years old. You see me and the Tane Mahuta - Maori for "Lord of the Forest" - the largest existing Kauri tree. North Auckland rainforest was full of these subtropical trees.

Cape Reinga
The meeting point of the Tasman Sea and the Pacific Ocean. From the lighthouse it is possible to watch the tidel race, as the two seas clash to create unsettled waters just off the coast. The Māori refer to this as the meeting of Te Moana-a-Rehua, 'the sea of Rehua' with Te Tai-o-Whitirea, 'the sea of Whitirea', Rehua and Whitirea being a male and a female respectively.
According to the Maori mythology, the spirits of the dead travel to Cape Reinga on their journey to the afterlife to leap off the headland and climb the roots of the 800 year old tree and descend to the underworld to return to their traditional homeland of Hawaiki, using the Te Ara Wairua, the 'Spirits' pathway'.
NZ's oldest stone building (1833)
NZ' oldest house (1822)
Lord of the Rings (LOTR) film location:
Edoras - capital of Rohan

Poor Knights Islands Marine Reserve Still to do!
One of the world's finest dive locations - off the coast from Tutukaka
Auckland Still to do, well some parts I have already seen, like the Harbour Bridge ... and I am not sure whether European have to visits cities in NZ. We have plenty of them in Europe anyway.

Coromandel Peninsula
I have only seen a tiny part of it. The beaches are beautiful for swimming, fishing and boating.

Lake Clearwater (Ashburton District): stunning views and the ridges mirror in the lake
Waitomo Caves Still to do!
See the glow-worms while black-water rafting. 
Farewell spit
Golden Bay
Cape Farewell  
Tahunanui Beach in Nelson
Eat fish in Mapua
Wharariki Beach
River Falls footbridge
Te Waikoropupu Springs
 (The clearest spring water in the world! Visibility of 63m!)
Harwood hole
(200m deep!)
 
Kaiteriteri beach
Abel Tasman Coastal Track
Mount Tarawera Still to do!
See the Buried Village and visit the museum and walk between the excavated dwellings.
Rotorua
The geothermal attractions (volcanos), including hot springs and mud pools. I missed the geysers.
White Island Still to do!
Take a cruise from Whakatane to NZ's most active volcano.
Lake Taupo
The sacred lake for the Maori. I did part of the so-called "Lake Taupo Challenge", a bike race around the lake (160km) ... but only did on leg of 40k.
Mount Taranaki Still to do!
This is the iconic picture of NZ. The volcano's perfect shape in a beautiful scenery.
According to Māori mythology, Taranaki once resided in the middle of the North Island, with all the other New Zealand volcanoes. Why he had to leave? Find out ourself and you will read a beautiful love story.
Tongariro Crossing Still to do!
Skiing in an active volcano
Wellington
Seen plenty of it: Te Papa Museum, seal colony, Embassy Theatre, Cable Car, Botanical Gardens, ...
Pancake Rocks blowholes Still to do!
Limestone rocks and blowholes that make a spectacular spouting display.
90 Mile Beach
Well, not really 90 miles long, but long and beautiful!
Franz Josef and Fox galciers

Arthur's pass crossing
Done with a camper van!
Mt Cook National Park
Still to do!
Tasman Glacier, the southern hemisphere's longest glacier, and Aoraki (Mt Cook), Australasia's highest mountain at 3754m.
Lake Tekapo Still to do!
Turquoise glacial lake best seen from the historic Church of the Good Shepherd.
See the Canterbury plains from Mont Hutt
Christchurch
Seen in 2010 before the two big earthquakes in 2011 and 2012
Visit Rakaia Gorge and Rakaia River
Curio Bay Still to do!
Fossilised forest which is believed to date from the Jurassic age.
Blue-eyed penguins of Oamara
Sunset in Hokitika
Stunningly beautiful!
French village in Akaroa and Bank peninsula
Watching the Hector dolphins in the sea ... 
Tramping in the Tararua Range Still to do!
Dunedin
 
Victorian and Edwardian architectur
Central Otago Still to do!
Only drove past it in a hurry!
Invercargill's Queens Park Still to do!
Queenstown Seen a bit in the summer and did not like it!
Probably the winter season is quite different. Still to do!
Lakes Wanaka and Hawea

Lord of the Rings movie-set locations
Well, I am not sure whether you can visit them all, but I have seen some.
Milford Sound
One of the most stunning places in NZ and on the earth. Bowen Falls, Stirling Falls, Mitre Peak! Watch bottlenose dolphins, fur seals, and Fiordland crested penguins.
Great Walks Still to do!
There are 9 great walks and the Whanganui Journey (a 4 day canoe trip).
Great Walk: Abel Tasman Costal TrackQueen Charlotte Track
Napier's art deco week
North Island's wine trail Still to do!
Only experienced part of Hawke's Bay and Martinsborough. Still have to check out Waiheke island, Kumeu, Matakana, and Gisborne.
South Island's wine trail Still to do!
Marlborough, Central Otago and the Waipara Valley.
Experience the first sunrise of the New Year as first person at the East Cape

Cruise around the Bay of Islands
Well, it was not really a cruise but a ferry trip from Russell to Paiha in the Bay of Islands.
Aoteaora's first capital
Waitangi Treaty grounds
One of the most important places in New Zealand history.
Manganui's fish shop
NZ's best fish and chips restaurant according to most Kiwis.
Cruise Fiordland Still to do!
Eat rock lobster at kaikoura Still to do!
Eat greenshell mussels
Done!
Eat Bluff oysters Still to do!
Walk on the longest wharf in NZ: Tolaga Bay
See the sacred mountain Tiruhanga
A Waka in the pasture
Hicks Bay
Oldest tree in Te Araroa
Scenic flight to the Southern Alps and the West Coast Still to do!
Bushwalking and tamping
Doing it all the time!
Moeraki Boulders
Maori legends explained the boulders as the remains of eel baskets and kumara washed ashore from the wreck of a large sailing canoe. This legend tells of the rocky shoals that extend seaward from Shag Point as being the petrified hull of this wreck and a nearby rocky promontory as being the body of the canoe's captain.  
Hot-air ballooning in the Canterbury region Still to do!
The TranzAlpine train journey
Spectacular journey, winding through amazing scenery. It is a great way to travel between Greymouth on the west coast and Christchurch on the east.
Still to do!
Travel in the Overlander from Wellington to Auckland Still to do!
Hot and cool pools of Ngawha Springs
The Maori chief Hone Heke took his injured warriors to this place known for its healing pools.
The hotest pool is 49 degree Celcius warm/hot. I could not even stand two seconds with only my toes in it!
Try catching trout or crayfish Still to do!
Experience Maori culture
This young Maori woman is training its mussles.
Bungy jump
Still to do, but I am not sure whether I really will do the jump! At least I aleady visited the bridge from where the first real bungy jump was performed.
Surfing

Island bay in Wellington is a nearby place to surf, but there are better spots in NZ: Opunake, Raglan, Piha, Muriwai or Ahipara, so still to do!
Te Anau glow worm cave
Haruru falls
Te Paki sand dunes
Do the haka
Kapiti coast
Watch the whales at Kaikoura Still to do!
Abel Tasman National Park
Cross Cook's strait in a sailing boat Still to do!
well, done by ferry!
Swimm with the dolphines, not just waching Still to do!
Take the Southern Scenic Tourist Route Still to do!
Sail through Doubtful Sound Still to do!
Tramp on Stewart Island Still to do!
Take the Alpine Pacific Triangle Tourist Route Still to do!
Take the Inland Scenic Tourist Route 72 Still to do!
Take Pacific Coast Highway Still to do!
Cape Palliser Still to do!
Weekend in Castlepoint Still to do!
Skiing on Mt Hutt
Skiing on Mt Ruapehu in the volcano
Drive up the steepest street in the world (in Dunedin) Still to do!
Visit Kapiti Island and watch the Kiwis Still to do!
Pelorus river and bridge
Climb Te Mata peak
Visit NZ's Longest Place Name: Taumatawhakatangihangakoauau-otamateapokaiwhenuakitanatahu

It means something like: The summit where Tamatea, the man with the big knees, the climber of mountains, the land-swallower who travelled about, played his nose flute to his loved one.