Taiwan is fairly expensive by Asian standards. Significantly cheaper than the most expensive Asian country, Japan, it ranks around 38 out of 300 most expensive places for expats to live. The cost of living in Taiwan can be as high or as low as you make it.
For a budget traveller, it is possible to get by on as little as NT$1000. A moderate restaurant meal should cost around NT$300. On the other end, a meal at the fanciest restaurant can be more than NT$1000 with accommodations costing over NT$5000.
For short term housing before you settle into a more permanent place, there area variety of hotels, sublets, and short-term housing.
Luxury Taipei Tienmu Apartment- features short term rentals in the premier residential area of Tienmu. Price is around US$120 per night for 4 to 5 people.
Contact: visitaipei@gmail.com (proficient in English, Chinese, Japanese)
Some other options include:
http://rentals.classifieds1000.com/Taiwan
http://taipei.craigslist.com.tw/hhh/
http://www.sublet.com
http://www.moveandstay.com
Update 10/12/2010