I have not established the beginnings of the Todd family but most research leads back to Scotland.

George Hortense Edwards stated in 1894:

"Of the nine distinct and so far as known wholly unconnected families of Todds in this country (the USA), three have come from Scotland direct, namely, the New York Todds, the Suffield, Connecticut Tods and (probably) the Philadelphia Tods;  Three have come from North of Ireland, Viz., the Maryland Todds, the New Hampshire Todds, and the Pennsylvania Todds; and three have come from England, Viz., the Massachusetts Todds, the New Haven, Connecticut Todds and the Virginia Todds.  Of these last three, the first two came from the republican or Puritan party, and the third from the royalist or Church of England party.  Of all the Todds in this country the Virginians were at first highest in social rank.
   The arms of the Todds, or of such as were authorized to bear them were, with trifling variations, Three fox head in red, in a shield, with a fox sitting, or running away with a goose, for a crest, and the motto, "Opertet Virvere"--- "One must live" (even if he has to steal for it.)"  ...  

    With a single exception the Todds have all come from the Highlands of Scotland." [Edwards 8]

p. 22 "What is known or the antecedents of the Todd family is most honorable. Of the covnanters captured at Bothwell Brigg [Bridge], two hundred and fifty were sentenced to be transported to America; and two hundred of these were drowned in the shipwreck of the vessel conveying them, off Orkney. They had been shut up below the hatches of the ship by the order of Patterson, the cruel merchant who had contracted for their transportation and sale. Fifty escaped and afterward took part in the defense of Londonderry.

Among those who were drowned were Robert Todd of Fenwick and James Todd of Dunbar. In 1679 -the year in which Robert Todd of Fenwick was drowned - John Todd fled from the persecutions of Claverhouse, in Scotland, to find refuge in the north of Ireland. Two of his grandsons, Andrew and Robert Todd, came with their families to America in 1737."[ Edward 22]