We routinely see lists of immigrant passengers coming to America published in newspapers.
Historical newspapers also published passenger lists of people going the other way—travelers leaving America.
Here is an old passenger list of people going to Ireland that was printed in the Irish American Weekly.
Irish American Weekly (New York City, New York), 10 May 1913, page 3.
This handy old newspaper article listed each passenger aboard the ship and where in Ireland they were going. Given that very small townlands in Ireland are specified, we can assume that these were likely Irish Americans going to visit family in the townlands where they had once lived. Historical passenger lists like this provide great genealogical clues for tracking down the specific places where your immigrant ancestors were born.
Some of the people visiting Ireland on this ship passenger list include:
• Miss Mary McCaffre: Belturbet, County Cavan
• Edward Devlin: County Armagh
• Miss Norah Gilroy: Ballisodare, County Sligo
• Mrs. Mary Reilly: Drumcalpin, County Cavan
• Mrs. Mary Gow and daughter Margaret: Westport, County Mayo
You can find almost everything in the old newspapers, including the journeys of your ancestors.