Go up (or photograph) Taipei 101. The 508 m tower's observatory shows the whole basin, and the 660-tonne golden damper ball inside is a sight of its own. Tickets run around NT$600 ($19). For the skyline photo with the tower in it, hike the 20-minute stair trail up Elephant Mountain before sunset — free.
Eat through a night market. Raohe and Shilin are the big two — grilled king oyster mushrooms, pepper buns, candied fruit and endless bubble tea. A filling dinner rarely crosses NT$200 ($6) per person.
Day-trip to Jiufen. This hillside gold-rush town of lantern-lined lanes and teahouses — often linked to the look of the film Spirited Away — pairs with the Shifen waterfall and old railway street, where visitors release sky lanterns. Tours or a bus-train combo make it an easy full day.
Ride the Maokong Gondola over tea plantations to hilltop teahouses, right beside the Taipei Zoo, and visit the National Palace Museum (around NT$350 / $11), home to the world's finest collection of Chinese imperial treasures — the jade cabbage is the celebrity exhibit.
Downtown, catch the hourly guard-change at Chiang Kai-shek Memorial Hall and the carved dragons of Longshan Temple. If you have an evening spare, soak in the Beitou hot springs, one metro ride from the city — the public baths cost under NT$100 ($3).