If you hold a US passport valid for at least six months from your date of entry to Taiwan, plus a valid return or onward air ticket, you can visit Taiwan without a visa for up to 30 days under the visa waiver scheme. You cannot extend your stay beyond 30 days under any circumstances if you enter Taiwan by this method. If your passport is valid for less than six months from your entry date, you can apply for a visa in advance, or on landing, at a cost of US$130 to 160.
Tourist medical facilities are widely available in Taiwan. Routine and emergency health care, for example, can be obtained from properly trained, English speaking physicians using the latest medical equipment. Taiwanese physicians will, however, expect immediate payment by cash or credit card, so it is worth checking that your regular health insurance covers you for medical expenses abroad and taking out extra cover if necessary.
One of the main attractions of Taiwan is its climate, which is warm all year round, with an average annual temperature of 72 degrees Fahrenheit. The weather during summer, June through August, and autumn, September through October is relatively stable, but plenty of rain can be expected during the southwest monsoon in the summer months. Typhoons also sometimes reach Taiwan, so it is worth keeping an eye on weather reports. Heat and humidity reach their peak in summer, so this is not the most comfortable time to visit. The Taiwanese winter (November through February) is mild and short, and any snow is restricted to a few mountainous areas. All things considered, the best time to visit Taiwan is between October and January. Within that period, religious and national days -- such as National Day on October 10 and the celebration of the founding of the Republic of China and New Year between January 1-3 -- are best avoided because of overcrowding and limited transport services.