Taiwan doesn't sleep - just look at the number of 24-hour stores out there. But since you have to....
For the budget-minded, there are hostels in Taipei and most other sizable cities. Camping is also available in many areas.
Motels æ±½è»æ é¤¨ can be easily found in suburbs of major cities. Despite the name, these have little if anything to do with the cheap functional hotels that use the name elsewhere; in Taiwan, motels are intended for romantic trysts and can be quite extravagant in decor and facilities. Many feature enormous baths with massage jets, separate massage showers, marble tiles, and so forth. Suites come with flat screen TVs as well as centrally controlled sound systems. During the daytime, most offer "rests" ä¼æ¯ of a few hours, and indeed check-in times for overnight stays ä½å®¿ can be as late at 10 PM. Taichung is considered the motel-capital of Taiwan.
Taiwanese hotels range in quality from seedy to very luxurious. Despite the complexities of doing business with both mainland China and Taiwan, most Western hotel chains operate in Taiwan such as Sheraton, Westin and Hyatt. Also, there are plenty of five-star hotels around. Keep in mind, however, that many of the international hotels tend to be outrageously expensive, while comparable and much cheaper accommodation is usually available in the same vicinity. For example, 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 away. Taxi drivers and tourist offices are invaluable resources for finding cheaper hotels.
Many hotels in Taiwan have both Chinese and Western names, which can differ radically. Find out and bring along the Chinese name in Chinese characters, as locals will usually not be able to identify the English ones. Especially when you visit the regions less traveled by westerners mostly because there is no business there, don't be shy to walk in on the more pricey hotels, especially off-season. The Ceasar å±æå¤§é£¯åº, the Chateau å¤é½æ²çé åº and the Howard Beach Resort ç¦è¯å¤§é£¯åº 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.
Hotel beds in Taiwan are generally much harder than in the West because of the old Asian tradition to sleep on a wood board. Modern mattresses can be found in most hotels, but only in the most upscale Western style hotels will you find beds in a real western style.