As a U.S. passport holder, you will be allowed to enter Taiwan without a visa for up to ninety days if your passport is valid for more than 90 days. If your passport has less than 90 days of validity remaining, you will be able to enter Taiwan for a time equal to the expiration date of your passport.
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Entry, Exit and Visa Requirements. Entry & Exit: Obtain a visa prior to arrival in the People's Republic of China (PRC) and have a passport with at least six months' validity remaining. The lack of either will result in a fine and immediate deportation upon arrival.
You must have a valid passport and an onward/return ticket for tourist/business visa free stays of up to 90 days. Your passport must be valid for the entire time you are staying in Japan. You cannot work on a 90-day visa free entry.
It's perfectly legal for Americans to travel to Cuba, except for explicit tourism purposes. However, you will need to meet some requirements. Specifically, you need a Cuban Tourist Card (a.k.a Cuban Visa), travel insurance, and a self-certification under one of the 12 travel categories of authorized travel to Cuba.
Crime: For most visitors, South Korea remains a very safe country. Common crimes occur more frequently in major metropolitan areas, tourist sites, and crowded markets. Take routine safety precautions. Pay attention to your surroundings.