Taiwan hotels
Taiwan doesn't sleep - just look at the number of 24-hour stores out there. But since you have to....
Taiwanese hotels range in quality from seedy to very luxurious. Keep in mind however that hotels which cater specifically to Westerners tend to be outrageously expensive, while comparable and much cheaper hotels are usually available, and most taxi drivers can take you to one. In particular, the airport hotel at CKS International charges about three or four times as much as a hotel in Taoyuan which is a half hour cab ride.
pMotels can be easily found in suburbs of major cities. A single room with attached bathroom will cost you about US$40 to 50 each day.
As in much of Asia, hotel beds in Taiwan are generally much harder than in the West. Only in the most upscale Western style hotels will you find beds any softer than a billard table.
For the budget-minded, there are hostels in Taipei and most other sizeable cities. Camping is also available in many areas.
Especially when you visit the regions less travelled by westerners (mostly because there is no business there), don't be shy to walk in on the more pricy hotels, especially off-season. The Ceasar, the Chateau and the Howard Beach Resort at Kenting, for example, located at one of the nicest beaches of tropical Taiwan, can be of exceptional value if you stay there during wintertime, as the rooms not yet let for the night are offered far below their normal price at last minute.