I stayed at Taipei Hostel last time. It's near to Shandao Temple MRT station which is one station away from Taipei Main station.
http://www.taipeihostel.com/

If you just want to tour around Taipei city, I believe this MRT map with places near to each station is very helpful. Many places can be easily reached by taking MRT. Check this map out.

I manage to write a few entries of my Taiwan trip on my blog, feel free to browse.
Chiang Kai-shek Memorial Hall
Shilin Night Market
Taipei 101
National Museum of History
Botanical Garden
Ximending

just buy a Universal Travel Adapter and you can use it in any country