Ten days on New Zealand's North Island: the half of the country the postcards skip

Auckland reads badly from the pavement, so get above it. The Sky Tower is 328 metres, the tallest free-standing structure in the southern hemisphere, and from the observation deck you can see the shape of the place: two harbours on either side of a narrow isthmus, volcanic cones scattered through the suburbs, and the islands of the Hauraki Gulf lined up to the north east.

Then walk five minutes downhill to the art gallery, which holds the largest collection in the country under a canopy of kauri and glass added in 2011. The rooms of Goldie and Lindauer portraits, painted from life in the late nineteenth century, are what people stand in front of longest.

Eat in Britomart near the ferries or walk uphill to Ponsonby, which has the better restaurants.

The Auckland War Memorial Museum stands on the highest point of a 75 hectare park that is itself an extinct volcano, and despite the name it is a general museum with Māori and Pacific holdings that have no equal anywhere. The centrepiece is a war canoe carved from a single totara log, more than thirty five metres long, kept indoors. Daily cultural performances run on the ground floor and are worth timing your arrival to.

Walk down through the park afterwards. The winter gardens halfway down are two Edwardian glasshouses around a sunken courtyard, free, with a fernery behind them in an old quarry.

Then a bus three kilometres south to Mount Eden, the highest natural point in the city at 196 metres, with a fifty metre grassed crater at the top and a full circle view. The crater floor is a sacred site and closed; the rim path is open, and the terraces cut into the slopes by a pre-European fortified village are still clearly there.

Both of today's destinations are across the water and the ferries leave from the same terminal.

Go to Devonport first, twelve minutes across the harbour, and walk out to North Head on the point at the harbour mouth. The whole headland was hollowed out between the 1880s and the Second World War and the tunnels, magazines and gun pits are open and largely unlit. Take a torch, go into them, and come out on the seaward side.

In the afternoon take the other ferry, twenty five minutes out to the island that fills the view north from the city. It erupted about six hundred years ago, which makes it the youngest volcano in the field and the only one that Māori living here saw form. There is almost no soil on it, the lava is bare and black underfoot, and what has colonised it is the largest pōhutukawa forest anywhere. The summit walk takes about an hour each way, and a signposted spur leads to a set of lava tubes you can walk through.

There are no shops on the island. Buy food and water before you get on the boat.

Collect the car and drive south. Allow three hours. The Matamata route carries less traffic than the main highway and passes through the Waikato dairy country, which is the flattest and greenest part of the island.

You will smell Rotorua before you see it. The town sits inside a collapsed volcano, steam comes out of the storm drains, and there are boiling mud pools in the public park.

Spend the afternoon in the geyser valley just south of town, where two Māori operations sit side by side on the same ground. The larger one holds the geyser terrace, where Pōhutu, the biggest active geyser in the southern hemisphere, throws water thirty metres up and does it repeatedly through the day, along with mud pools, a national carving and weaving school that trains Māori artists, and a kiwi house. The guides are from the valley.

Book a cultural evening for tonight if you want one: a welcome onto a marae, a concert, and a meal cooked in the ground.

Start next door to yesterday. The thermal village on the same field is where about twenty families still live on top of the geothermal system: they cook in steam boxes and boiling pools in their gardens, they bathe in the springs, and the tour is led by residents through the streets they live in. It is less produced than its neighbour and rather more affecting. Buy the corn boiled in a hot pool.

Then drive twenty five minutes south to the loudest of the geothermal parks: a bright orange and green spring called the Champagne Pool, sulphur terraces in colours that look adjusted, and collapsed craters, on three looped walks. The geyser at the entrance erupts at a quarter past ten each morning, reliably, because a ranger drops surfactant into it.

Finish in the mineral pools at the edge of the lake. There are twenty six of them in four sections, fed by two springs: an alkaline one that comes out between thirty six and forty two degrees, and a much more acidic one that a Catholic missionary claimed cured his arthritis in 1878. Several look straight out over the water. Go at dusk.

It is an easy hour south to Taupō, so there is no need to leave early.

Stop on the way in at the falls just north of the town. The Waikato River, which drains the whole lake, runs wide and slow until it is forced into a channel about nine metres across, and the entire flow, something like two hundred thousand litres a second, goes through it and drops eleven metres into a pool that is an extraordinary shade of blue. There is a footbridge directly over the throat of it. It is the most visited natural attraction in the country and it deserves to be.

Then the steam field five minutes further on. A gravelled path loops for about three quarters of an hour past steam vents, spitting craters and ground so hot the vegetation has been cooked back to scrub, with cloud blowing across the boardwalk in a way that makes the whole thing feel less like a park and more like a fault. It is at its best on a cold morning.

Get into Taupō in the afternoon and look south. The lake is thirty five kilometres across and on a clear day the volcanoes are on the far side of it.

The dam a few minutes up the road holds back a gorge, and four times a day, on a schedule, the gates are opened and the whole river is let through in a controlled flood. It fills a dry rock canyon in about five minutes, runs for half an hour, and then drains away again. There is a rail above it and a bridge across the gorge. Get there fifteen minutes early.

Then carry on another twenty five minutes north to the hidden valley, which is reached by a boat across a reservoir and is the least visited of the region's geothermal parks and, for a lot of people, the best. A boardwalk climbs through silica terraces, geysers, and a cavern with warm water standing in the bottom of it that people have bathed in for centuries.

Come back to town in the late afternoon and use the lake. The water is cold and clear and there is a stretch of black sand beach in the middle of Taupō.

This is the long drive, a bit under four hundred kilometres, and it is also the best road on the island. Ten minutes south of Taupō the highway climbs onto the volcanic plateau and runs for fifty kilometres across open tussock with three live volcanoes on the right: Ruapehu, which is 2,797 metres and carries a crater lake and a ski field, Ngāuruhoe, which is the near perfect cone that stood in for Mount Doom, and Tongariro behind them. There is nothing else out there. It closes in winter snow, so check.

After that the road drops through farmland and follows the coast down to Wellington.

Arrive, drop the car, and give what is left of the day to Te Papa on the waterfront. It is free, it is the national museum of a country that has thought hard about what one should be, with Māori and Pākehā histories told alongside each other, a marae inside the building, an earthquake house that shakes, and the only complete colossal squid on display anywhere. The war exhibition on the second floor, with figures at two and a half times life size, is the one people come out of quiet.

One continuous downhill walk with a lift at the start, and the best half day in the capital.

The cable car has run since 1902 and climbs out of the middle of the shopping street to the ridge at Kelburn in five minutes. Pay for the trip up only; the point is to walk back down.

You come out at the top of the botanic garden, twenty five hectares falling down the hillside: native bush at the top, a rose garden and duck pond in the middle, and at the bottom an old colonial cemetery that was cut in half by a motorway in the 1960s, with the graves moved and a footbridge thrown over the road.

That drops you in front of Parliament. The complex is four buildings, the best known of which is the Beehive, a 1970s executive wing that looks exactly like its nickname and divides opinion permanently. Free tours run through the day; you leave your bags at the visitor centre and clear a checkpoint.

Mount Victoria is 196 metres, about an hour's walk up through the Town Belt or ten minutes by car, and the view is a full circle: the harbour, the airport runway between two stretches of water, the centre below and Cook Strait beyond. Wellingtonians drive up here at night just to sit and look at it.

Come down along the waterfront to Oriental Bay, a curve of imported golden sand with a jetty and a row of cafes facing north into the sun. It is the sheltered corner of the harbour and the last easy hour of the trip.

The airport is fifteen minutes from there. If you are carrying on to the South Island instead, the ferry terminal is on the other side of the centre and the crossing to Picton is most of a morning through the Marlborough Sounds.