Harrison/Murphy/Driscoll - From Cork to Boston to New York

Hi, My Harrison ancestors were in Cork City in 1861.  Next record I have of them is in Brooklyn, New York in 1870.  Story I heard is they came into Boston and then made their way down to New York.  Has anyone heard of this and how would they have traveled from Bston?  I have been unable to find any immigration records.  Any suggestions?  Thank you.  Kevin Harrison