Looking at arguably the five great ballet choreographers to date:
August Bournonville: Danish-born, but his father emigrated to Denmark. He was trained by the Italian Galeotti and the French Vestris, and he lived and studied in Paris for five years. He had an aunt at Royal Swedish ballet, I assume through his Swedish mother.
Marius Petipa: French-born, raised partially in Belgium, also trained under Vestris, spent three years in Spain, moved to St. Petersburgh to dance at 29, where he worked with Perrot for almost a decade to learn his craft.
Frederick Ashton: Grew up in Ecuador and Peru. His early ballet influences -- Pavlova, Massine -- were Russian.
Antony Tudor: British-born, but his career was primarily at ABT and in NYC wherever he taught. Technically, he was from the Italian school of Cecchetti, whose artistic lineage goes back to Beauchamp, and, after becoming London-based, had a profound influence on ballet schooling in Great Britain and the colonies.
George Balanchine: Trained at the Imperial School, went to Paris, London, Copenhagen until Kirstein convinced him to come to America, where for over a decade, he mainly choreographed for American musicals and films.
Bournonville was the only one to stay where he was born for most of his life. The rest were peripatetic until they landed in what was to become their long-time artistic homes. There were a lot of shake-ups and "foreign" artistic influences in their lives.
Great American male dancers are yet another thread.
Edited to add: the whole categorization seems arbitrary when you think of kids like Aran Bell, for example. If he wasn't born on US soil, it's likely he was born on a military base or in a local hospital providing services to the military. However, he's been largely trained by Denis Ganio. I believe both Julian and Nicholas MacKay and raised in the US until they joined the school of the Bolshoi Ballet school, where they are studying through the pre-professional track, and not as a one or two-year finish to an otherwise US dance education. Michaela DePrice was born in Sierra Leone and was adopted as a young girl. Her life fits into one of the classic American narratives, but as she wasn't US-born, it seems like she couldn't count.