Ann Cavanaugh, of Ohio/Ireland

My resolution for this year is to try to find out more about Ann Cavanaugh, who married James Meagher in Massillon, Ohio, in 1862. I'm hoping that some reader of this post may be able to help. For most of the branches on my family tree we know exactly which townland in Ireland or which town/village in Hungary was the ancestral home. But for Ann Cavanaugh it is only a guess, probably a good one, that either Ann or her parents came from somewhere in Ireland. (My Brooks-Humbertson branch also has uncertainties, but those uncertainties predate Ann Cavanaugh by at least a generation.)
It is a common name, and so it will be difficult to identify the correct Cavanaughs. Probably the most reliable information about Ann was provided by her oldest son, Patrick (a great-grand-uncle of mine). When one of Patrick's younger brothers, James, died in 1931, Patrick provided the information for the details on his brother's death certificate. Patrick reported that their mother, Anna Cavanaugh, was born in Massillon, Ohio. That birthplace is consistent with both the 1860 and the 1870 census records, which show that Ann was born in Ohio. In 1936 when Patrick himself died, Patrick's son Daniel reported that his grandmother was born in Ireland. That Daniel thought his grandmother had come from Ireland provides some basis for assuming that Ann's ancestry was no more than two generations removed from Ireland.
Ann's husband was, of course, a first-generation immigrant from County Tipperary. As a still single man in 1860, James Meagher was a coal miner living in Mineral City. As a married man in 1870 and 1880, James and his family were living in Mineral City. But I suspect that Ann and the older children had spent considerable time in Massillon during the 1860's. Both Patrick, the oldest son, and my great-grandfather Thomas Meagher, the second oldest son, were familiar with their Massillon origins. Father James himself could perhaps have found alternative employment in Massillon during the early years of his marriage, before eventually settling back to coal mining in Mineral City. It's even conceivable that James could have commuted from Massillon to his work near Mineral City. Still it's reasonably clear that the connection to Massillon was through Ann's side of the family.
A Thomas Cavanaugh was a witness for the wedding in 1862. Thomas would have been the name of Ann's father, if the Meagher-Cavanaugh family followed the traditional naming conventions, which they did in fact follow for the names on the Meagher side of the family. (This Thomas Cavanaugh would be the namesake for many contemporary Thomas relatives of mine.) Ann could have incorrectly remembered being born in Massillon, but if so she probably at least had arrived there at a very young age accompanying her parents. If Ann was in fact born in Massillon, it is still probably the case that her parents were relatively recent arrivals there. Census records have Ann a decade younger that her husband, so her parents could have emigrated either well before the Famine, or at the very beginning of it. Possible itineraries are described in the history of Massillon's St. Mary parish:

The majority of the early Catholic settlers were of German heritage. ... They had come overland through Pennsylvania, or had arrived in the United States and proceeded by boat from New York, up the Hudson River to Albany and then westward on the Erie Canal to Lake Erie, Cleveland, and then southward on the Ohio and Erie Canal to Massillon. With the building of the canal through Massillon, there was an influx of Irish immigrants. They labored in building the canal and also worked in the local coal mines. ...