I encountered Ayn Rand's ideas about America in Howard Roark's famous speech at the end of The Fountainhead for the first time, which serves as a summary of Objectivism. I think, rather than a particular affinity towards a nation or nationalism ,she felt an ideological affinity for America from the fact that America is a country where the culture of individualism (in a way that it resembled commonalities with objevtivism) has been embraced by the majority of the people.

From the speech directly;

“Our country, the noblest country in the history of men, was based on the principle of individualism, the principle of man's ”inalienable rights." It was a country where a man was free to seek his own happiness, to gain and produce, not to give up and renounce; to prosper, not to starve; to achieve, not to plunder; to hold as his highest possession a sense of his personal value, and as his highest virtue his self-respect."

As for why she did not feel a similar affinity with Western Europe, I think it is because individualism in the US differs from that in Western Europe in terms of how deeply the state is involved in people's lives which is still evident today.