I went to Taipei (Taiwan) for a short 4d3n stay last month and stayed at The Fun Hostel Taipei. This is my review of the place. Fun Hostel has a few branch around Shilin area so don't get confused by the different address.
Name: Fun Taipei Hostel
Address: No.5, Xiaobei Street, Shilin District, Taipei, Taiwan
Tel: +886-2-28881112 (Overseas), 02-2888-1112 (Domestic), 2888-1112 (Public phone in Taipei City)
Room type: Dormitories. Bunk beds in separate rooms.
Nearest MRT: Shilin MRT
Nearby attractions: Shilin Night Market & National Palace Museum (via bus)