Although most people try to fuse them into one, it appears there were actually two David Harbisons in southwestern Virginia, abotu the time of the Revolutionary War. I'll focus first on the eponymous David, because for him we have the enormously useful Harbison-Carr family bible, in the possession of the State of Virginia but available online.
The same David is mentioned in Kentucky: A History of the State, Battle, Perrin, & Kniffin, 6th ed., 1887, Shelby Co.
WILLIAM SCOTT HARBISON was born in Shelby County, Ky., February 17, 1816, and is the second son of William and Elizabeth (Mahon) Harbison. His grandfather, William Mahon, was a Presbyterian minister. He came from Virginia to Boyle County, Ky., in 1796, and died at the age of sixty-three in Marion County, Ky. David Harbison, paternal grandfather of W. S. Harbison, came from Ireland about 1778, with wife and infant son, James, remained a while in the State of New York, and then moved to Wythe County, Va., and settled on a farm. Before leaving Virginia, in 1805, four more sons were born: David, Samuel, John and William, who at that time were all grown up, and large men, none under six feet, and Samuel was six feet six inches. The eldest son, James, married and remained in Virginia. The other four came with their father to Kentucky; all are now dead. They stopped one year in Fayette County, Ky., and in 1806 moved to Shelby County and bought a farm near Shelbyville. The grandfather died aged ninety-one years. His wife, Esther, died aged seventy-five. He and all his sons were sober, industrious, strictly Sabbath keeping and successful business men. William Harbison, father of W. S. Harbison, was born August 15, 1785, and died August 20, 1826. He served on campaign as an officer in the war of 1812, or 1813, and his brother, Samuel, served two campaigns in the same war as captain.
Here are the children, as listed in the family bible.
It is hard to credit the earlier dates in this account. New York was under the control of the British from 1776 until 1783. The British would not have been inclined to allow a young family to land and then cross the Hudson, New Jersey, and the Delaware, and across southern Pennsylvania and Maryland to the Shenandoah Valley. Far more likely David immigrated earlier, perhaps even before James was born, although it is possible David and his family were detained in New York until after the peace, at which point they made their way south to Virginia. Wythe County, by the way, did not exist until 1790. Before then is was the now extinct Fincastle County. In support of the earlier arrival hypothesis, Baxter D. and Davis Harbison, sons of David, both list their father's birthplace as Virginia in the 1880 and 1900 censuses.
Other than this, the Kentucky History seems to be accurate. David, Esther and their four youngest sons migrated to Shelby County, KY, in the mid-1800s. James remained in Virginia, in Wythe County when it was formed in 1790, and had three daughters, all of whom married, Eliza, who married Thomas Jefferson Adams and died in Loudon Co. Tennessee in 1854; Esther, to John Carr on Mar 27 1823, and Polly, to William Wyson, in 1825.David seemed to live with his son Samuel in 1820 and 1830; Esther died in October 1824.