We should no longer be an immigrant nation. We have enough here already. Instead we should change the requirement to be president to allow only a third generation to hold the office. That would allow immigrant to be come a citizen, have children who are a citizen, and then the grandchildren be eligible. Since the chance of becoming President is about one in 230 million, that's not really discrimination either.
Fiorello LaGuardia, Ahhnold Schwartzenegger (who really does seem to have done the best job he could in much beset California), Henry Kissinger (electable early on before the invasion of Cambodia), former UN Ambassador John Negroponte. Note that they are all Republicans.