Taipei Food & Sights
Ningxia Night Market
Probably the most famous night market. View on map
It is known for the oyster omelet. The Michelin oyster omelet had a huge queue; we went to this other stall and it was really good: Oyster omelet (map).
My favourite stall: Map. I had the tomato with the south Taiwan sauce — the freshness of the tomato complemented the sweetness of the sauce.
Hikes & Views
Hike up Xiangshan (Elephant Mountain). It's a short but steep hike (about 30 minutes) with awesome views of Taipei 101.
For a more substantial hike accessible by public transport, try Yangmingshan (shan 山 means mountain). You can take a bus to the trailhead; there are often wild cows. It's close to Beitou so you can visit a hot spring afterwards.
Museums
The National Palace Museum has impressive jade stonework exhibits and a lot of porcelain: Map
Tamsui
Tamsui is where the river meets the sea. It has a cute old street and preserved colonial buildings: Map
The highlight is cycling along the river in a dedicated lane and crossing a bridge above the mangroves — very impressive: Cycle route
Great place to watch the sunset; there are lots of small bars that serve cocktails: Sunset bars
Nightlife Areas
Area with a lot of bars:
Also in this area they sell dou hua (Taiwanese dessert) — not too sweet, goes well with ice and sugar syrup or ginger: Dou hua (map)