Check out the following mid-range accommodation in Taipei (1500NT$-3000NT$ per night) :

• Fullerton 41 Hotel (Daan District)
• Emperor Hotel
• Y Hotel 
• Good Ground Hotel  (close to Taipei Main Station)
• Holiday Inn East Taipei Hotel  
• City Inn 1 and 2 (close to Taipei Main Station)
• Keymans hotel chain (close to Taipei Main Station)
• See you Hotel (close to Taipei Main Station)
• Miyi Hotel (close to Taipei Main Station)
• TS hotel (close to Ximending)
• Forte hotel chain
• Friends Hotel (close to Sogo)
• Dreams House (close to Taipei Main Station)

Up-scale hostels (1000-1500NT$)

• Mudan House (great reviews, 2 stops north of Taipei Main Station)
• Taipei NTU House (NTU NTNU Shida Area)

There are several other cheap mid-range options on wonderful Dayrent website (in Chinese)

If you can't find what you're looking for here, try this list of Taipei hotels.