In the earlier part of your time period (which was before steamships), it might take months. Sailing ships were very dependent upon the wind. At the end of your time period, perhaps it took three weeks. Steamships became faster and faster after 1880.
Also, once they arrived in the U.S., they had to travel by land (trains, perhaps; or think of the old stagecoach days or think of getting on a river boat, etc.) to get to Galesburg. Perhaps some early histories of Galesburg will suggest how the early settlers arrived there.