Ten days in Taiwan: down the east coast and back up the west, all on the train

Taipei 101 was the tallest building in the world from 2004 until Dubai took the title, and the city is still arranged around it. The observation deck is on the eighty ninth floor and the lift gets there in under forty seconds.

The better view is from the hill fifteen minutes east. Elephant Mountain is a steep flight of steps into subtropical forest, and the platforms near the top put the tower dead centre with the whole basin behind it. Go up an hour before sunset; the path is lit on the way down.

Then eat. The nearest night market is ten minutes from the tower, smaller and more local than the famous ones, which makes it a good first one.

When the Nationalists lost the civil war in 1949 they took the imperial art collection with them: Song ceramics, Shang bronzes, Tang paintings, crated up and shipped across the strait. It is still on a hillside north of Taipei and only a fraction is on show at a time.

Go early, ideally on a weekday. Tour groups arrive mid morning and the two most famous objects, a jadeite cabbage and a piece of jasper carved into pork belly, get a queue of their own.

In the afternoon drop down to Dalongdong, where a Taoist temple built between 1805 and 1830 has the finest painted and carved decoration on the island. Shilin, the night market everyone means when they say night market, is a few stops south.

Wanhua is the oldest part of the city and Longshan Temple is its centre. Founded by settlers from Fujian in 1738, flattened by Allied bombing in 1945 and rebuilt, and busy with people praying at every hour.

Time it for a chanting session. Several hundred people reciting together under the incense is the single most memorable thing in Taipei.

Bopiliao, five minutes away, is a block of restored nineteenth century shophouses and the best surviving picture of the streets the temple grew up in.

The afternoon goes east to the Chiang Kai-shek memorial, which is both a national monument and an argument the country is still having with itself. The flag comes down at sunset.

Two to three hours from Taipei Main Station, and for the second half of it the line runs between the mountains and the Pacific with almost nothing in between. Sit on the left going south.

Hualien is small and low and slower than anywhere on the west coast, with a large indigenous population. The old railway workshops in the middle survive as a small museum to the narrow gauge line that once ran the whole east coast.

A Japanese officers' villa sits in a garden of pines above the harbour, built during the occupation and now a quiet gallery with a view over the water.

Then the night market, where the back lane belongs to indigenous stallholders and is the reason to come.

Leave by seven. The gorge road climbs west from the coast and the first stop is fifteen minutes past the entrance arch, so an early start buys you an hour of it to yourself.

The order that works is west along the road, stopping as you go, then back down. Shrine over a waterfall first, then the narrowest section where the cliffs almost meet over the road, then the trail that runs along a ledge above the water.

Everything here is marble. The river has cut through a mountain of it, and the water below is a colour that photographs badly and is genuinely that green.

Take a picnic. There is one small settlement halfway up with food and otherwise nothing.

Four hours south through Taitung and round the tip of the island, on the least travelled and best looking railway in Taiwan. Rice terraces on one side, the Pacific on the other, and a tunnel every few minutes.

You arrive in a working port city that spent a century on containers and petrochemicals and then gave its waterfront back. Start underground, in the metro concourse that has a stained glass dome hanging over it.

Pier 2 is fifteen minutes away: blocks of dock warehouses turned into free galleries, with a light rail and a bike path along the quay. Stay until dark, when the cranes are lit.

The tourist night market near the main station is a short metro ride and does the job for dinner.

Lotus Lake is north of the centre, one stop from the high speed station, and its shore is crowded with temples that stand on causeways above the water. Go early and walk or cycle round it in an hour.

The pair everyone comes for are the Dragon and Tiger pagodas. You go in through the dragon's mouth, walk the length of its painted body and come out through the tiger, which is supposed to turn bad fortune into good. Backwards is meant to be unlucky, so watch which end the queue is at.

In the afternoon go to the harbour mouth, a narrow channel with a hill on one side and a sandbar island on the other. The ferry to Cijin takes five minutes and the far side of the island is a long grey beach facing the Taiwan Strait.

Eat on Cijin. The street opposite the pier is tanks and grills, and you point at what you want.

Forty minutes north on an ordinary train and you are in the middle of the oldest city on the island, and the one every Taiwanese will tell you has the best food.

Chihkan Tower is what the Dutch called Fort Provintia, built in 1653 and taken by Koxinga nine years later, with Qing pavilions raised over the original brick base that is still there under your feet.

The temples around it are the point of the afternoon. Tainan has more of them than anywhere else in Taiwan and they are all in use, with divination blocks clattering on the floor and incense going constantly.

Eat early and often. The stalls with queues at five in the afternoon are the ones to join.

Anping is where the Dutch landed and where the sea used to be. The harbour silted up long ago and the fort sits inland now, but the district still feels like a port: low houses, drying racks, shrimp cake shops and canals.

Fort Zeelandia is the anchor. The Dutch held out here for nine months against Koxinga before surrendering the island in 1662, and what survives is a wall of brick set in oyster shell mortar with a later lookout on top.

The tree house nearby is the thing people remember. A trading company warehouse was abandoned in the 1940s and a banyan moved in, so the roots hold the walls up and the roof is leaves.

Back in town for the evening, the temple quarter is where Tainan actually lives.

Two sites five minutes apart close the loop on everything you have walked through. The Confucius temple was founded in 1665, the year after Koxinga's son consolidated the family's rule, and it was the island's first school.

It is a walled compound of low red halls under old trees and it is quiet in a way that nothing else in Tainan is. The shaved ice shop across the road has been there for generations and counts as part of the visit.

Koxinga's shrine is a short walk away, and he is the most contested figure in Taiwanese history, claimed in turn by the Qing, the Japanese, the Nationalists and Beijing.

The shuttle to the high speed station takes twenty minutes and Taipei is ninety minutes after that.