Portuguese sailors are supposed to have named Taiwan Ilha Formosa in the sixteenth century. That's the story, anyway. Taipei, the capital, sits in a bowl of volcanic hills in the island's north. It rains a lot. People carry umbrellas the way others carry keys, and the city keeps going. The best way to see it is to give it one full day and start early.

5:30, Elephant Mountain
Take the metro to Xiangshan station and walk to the trailhead. The stairs are steep. Twenty minutes, less if you're fit, and expect to be overtaken by retired men in tracksuits who do this every morning. From the rocks at the top you look straight across at Taipei 101. On a cloudy morning, the tower disappears somewhere around the fortieth floor, which is its own kind of view. Breakfast afterwards: warm soy milk and youtiao, long fried dough sticks.

8:00, Longshan Temple
Longshan Temple has its own metro stop, which tells you how much it matters here. Settlers from Fujian built it in 1738. It has burned, cracked in earthquakes and taken a direct hit from Allied bombs in 1945. The statue of Guanyin in the main hall survived that raid, and people still talk about it. Watch the red wooden blocks shaped like half moons. Someone asks a question, drops the pair on the floor and reads the answer from how they land. One flat side up and one round side up means yes.

11:00, Dihua Street
This is old Taipei. In the 1800s, the Dadaocheng district shipped tea and camphor down the river, and merchants built tall shophouses with carved fronts that still stand. The ground floors sell dried shiitake, scallops, herbs, fabric and a surprising amount of dried fruit.

Halfway along is Xiahai City God Temple. It's small. People come for Yue Lao, the god of marriage, who is said to tie a red thread between future couples. Many come back later with wedding candy for him.

14:00, Beitou
Change at Beitou station for the short branch line to Xinbeitou. You'll smell the sulfur before you see anything. Thermal Valley, at the top of the park, is a steaming green pond too hot to touch. On the way down you pass the public library, a wooden building with a planted roof.

The open-air public bath near the stream is mixed, so bring a swimsuit. Hotel baths are usually separate for men and women, and there you go in with nothing on. An hour is plenty. You'll come out heavy and slow, which is the idea.

17:00, Maokong
Getting here from Beitou takes over an hour, right across the city to Taipei Zoo station. Then the gondola. If you don't mind a longer queue, wait for a cabin with a glass floor.

Maokong grows tea, mostly Tieguanyin and Baozhong. Teahouses along the road brew it in small clay pots, and many also cook with the leaves. Find a terrace, order a pot and stay until dark, when the basin below fills with lights.

19:30, Für Elise in the Lanes
Taipei has almost no public bins. Garbage leaves by truck, and every truck plays music so people know it's coming. Usually Für Elise. Sometimes A Maiden's Prayer. Whole lanes empty out when they hear it, people carrying bags and sorted recycling, a few in pyjamas. Two minutes of chatting at the curb, then the truck moves on.

21:00, Raohe Night Market
The entrance is at Ciyou Temple, right by Songshan station. The first queue you'll see is for pepper buns. They're baked stuck to the inside wall of a clay oven and come out stuffed with pork, lots of black pepper and scallion. Everyone burns their mouth on the first one. Then keep walking: herbal pork rib soup, grilled squid, stinky tofu if you're brave, shaved ice to finish. Raohe is a single lane about 600 meters long.

23:30, Taipei 101
At this hour, the observatory is closed, so you look at 101 from the street. It's 508 meters tall, finished in 2004, and it held the title of world's tallest building for six years. The design follows bamboo: eight sections of eight floors each, because eight is a lucky number in Chinese. Near the top, a 660-ton steel ball hangs on cables to steady the tower in typhoons and earthquakes. The lights change colour by weekday. It's red on Monday, then cycles through the rainbow to purple on Sunday.

Magelline Perspectives
We think Taipei works best without a tight plan. Everything here is close to a metro station, the city feels safe late at night, and the convenience stores never close. Pack an umbrella. Leave room for a second dinner.