In short
Taipei is a dense capital set in a basin ringed by volcanic mountains, which explains both its humidity and the disconcerting ease with which you pass from city to forest.
Xinyi is the modern district, around Taipei 101. Zhongshan and Datong keep the older architecture and the lanes. Ximending is the youth quarter. Beitou, to the north, is a hot-spring district linked by metro.
Arriving and getting around
Taoyuan airport is linked to the centre by a dedicated metro line in about forty minutes. Songshan, in the city, serves domestic and regional flights.
The MRT is clean, punctual and simple. The EasyCard works on the metro, buses, YouBike share bicycles and in convenience stores.
The high-speed train runs down the west coast and reaches Kaohsiung, at the other end of the island, in under two hours.
What it really costs
Taipei is markedly cheaper than Tokyo or Seoul, particularly for food.
The night markets are the city's catering system — Shilin, Raohe, Ningxia — not a folkloric curiosity. You dine there for very little.
When to come
October–April is the best period: dry and temperate.
Summer is very hot and humid, and typhoon season runs from July to October: warnings close transport, shops and government offices, sometimes for a whole day.
What nobody tells you
Eating and drinking are forbidden on the Taipei metro, water included, and the fine is enforced. The rule surprises visitors arriving from elsewhere in Asia.
Beitou is a hot-spring district reachable by metro: public and private baths, twenty minutes from the centre. The Hokutolite found there is globally rare.
Jiufen, a terraced village on the north-east coast, is the classic day trip. It is saturated at weekends; on a weekday and late in the day it becomes workable again.
7-Eleven and FamilyMart are extremely dense and serve every purpose: paying bills, collecting parcels, buying tickets. They are infrastructure, not merely shops.
Taipei is noted for a high level of safety, at night included.