Secure American Foreign Evacuation Act This bill requires U.S. citizens and permanent residents who visit or reside in highly dangerous foreign countries to register with the Department of State. The President must submit to Congress within 30 days a list of highly dangerous foreign countries. These are countries (1) whose government has repeatedly provided support for international terrorism, (2) where U.S. armed forces have engaged in hostilities, or (3) where there is a high probability that U.S. citizens or permanent residents visiting or residing in the country will need to be evacuated. The President must periodically update this list. Within five days of departing the United States or another foreign country to visit or reside in a highly dangerous foreign country, a U.S. citizen or permanent resident must register with the Department of State. Failure to comply with the registration requirement results in a financial penalty, which the State Department may waive in extraordinary circumstances. When evacuating U.S. citizens and permanent residents from highly dangerous foreign countries, the United States shall give priority to those who have complied with the registration requirements. The State Department must report on the implementation of the registration system and give recommendations for its improvement.