Re: McNally origins in Irish counties

McNally is generally believed to be an Ulster name.Cavan is part of the Province of Ulster, though it's now in the Republic of Ireland.I know there are a number of McNallys in Mayo, but I believe the majority of McNallys are from the eastern part of Ulster.My own have origins in Tyrone.
Was your gggrandfather married in Illinois?Did he die there?
You might look for civil records.They may give his county of birth in Ireland.Another idea would be to check his children's birth certificates to see if his place of birth is listed.Did he become a US citizen?Sometimes place of origin is given in those records.
Illinois has very good online genealogical records.