Timur Bekmambetov is an example of a Russian director (”Wanted” and “Abraham Lincoln: Vampire Hunter”) though the budgets of his films aren’t anywhere near $200 million.
Jee-woon Kim is a Korean director who did the latest mummified corpse, er, I mean, Arnold Schwarzenegger film “The Last Stand.” Estimated budget was $30 million.
There may be other examples, but not many. A foreign director has to REALLY stand out in order to get a big U.S. film. John Woo and Robert Rodriguez probably the most prominent examples I can think of.
Robert Rodriguez was born in San Antonio.