The New York Times has a really neat interactive map which shows dominate immigrant group by county. The data can be viewed by decade from 1880 to 2000 and is based on the census.
One interesting thing to see is the new wave of immigration, primarily from Latin America, that only got started in the 1970s and made a huge jump in the 1990s. Another interesting thing is that the collapse in immigration from Europe in terms of percentage is only a recent phenomenon. Finally, look at how soon immigration trails off in the South. An isolationist culture combined with little industry kept the American South from booming in ways the rest of America did.