Finally, in October 1979 he was allowed into the U.S., where he was treated (unsuccessfully) for advanced lymphatic cancer at Cornell Medical Hospital in New York City. His friendly reception in the U.S. sparked outrage in Iran, where radical students retaliated by taking over the U.S. Embassy in Tehran and holding embassy workers hostage for 444 days. Hoping to take political pressure off the U.S., the dying ex-monarch next traveled to Panama, a U.S. ally with modern medical facilities. But the Panamanian government was ambivalent, and even considered extraditing the Shah to Iran to face charges of murder and torture during his reign. Hoping to avoid this final indignity, the Shah returned to Egypt, where he died in Cairo on July 28, 1980.
Read more about the Shah and seven other dictators in exile at mental_floss. Link