Of the "Four Beasts" hiking trails that wrap around the southeast corner of Taipei, Elephant Mountain (Xiangshan) is by far the most popular — a 20-minute stone-step climb from the eponymous MRT station that brings you out on a viewing platform almost level with the upper floors of Taipei 101. The classic photograph of 101 at sunset, taken from the boulders just above the top platform, is taken here every evening by half the visitors in town.
Carry on past the platform and the trail loops along the ridge with several more vantage points and many fewer people. Wear proper shoes — the steps are steep and uneven. Sunset is the best time; bring a torch for the descent.