Good question. The last chapter of Trotsky's autobiography "My Life" was called "Planet without A Visa". Lev Davidovich had trouble getting a visa to any country. The British wouldn't let him in (despite Betrand Russel, I think, trying to pull strings) and that included everywhere the British controlled. Same goes for the French, the Gerrmans, the Soviets. Because of his revolutionary background the European democracies didn't want him.
Maybe Brazil or elsewhere in Latin America? Trotsky thought developments in the US would be important and he wanted to get as close as he could to the USA.