All data drawn from 1880 IPUMS for the USA:
In order to get a sense of how population migrated between 1820-1880, we compare the 1880 county of residence of all persons 40 years old and older with the birthplace of their parents. The birthplaces of parents shown in the following maps are US states and the most important foreign countries. In 1880 the largest immigrant groups were from Ireland, Germany, and Scandinavia.
There is a remarkable tendency for migration to stay close to the latitude of the source state. The resulting migration trace typically moves due west, though eventually fanning out.
With the exception of Illinois, which contributed to the settling of Arkansas and Texas, most migration from the following states looks like a smoke plume generated by a strong wind from the East.
New Mexico and California contained large and long-established Latino populations. There was also significant immigration of populations speaking Romance languages from Latin America and Southern Europe. Canadian immigration was quite strong along the northern border.
The largest immigrant populations came from Ireland and Germany. Immigration from Great Britain was especially important in the West. Scandinavians settled west of the Great Lakes and were also an important component in the emerging Mormon population of Utah.
The Netherlands and Switzerland were locally important. Immigration from eastern Europe was not to become large scale until late in the 19th century. Chinese immigration was quite significant in the West. It was fairly common among blacks to have a parent born in Africa.
In the following maps, counties where most of the movers were white are shown in red-scale, while counties where most of the movers were black are shown in green-scale. There is a clear pattern of black migration from tobacco-growing states, such as Virginia and North Carolina, to cotton producing areas. White migration heads almost due West, though fanning out at a distance.