The location here is near President Lincoln's Cottage at Soldiers' Home. The guard at the home heard the shot and Lincoln ride up shortly after so we know the site of the attempt was close. The site also had to be south of the home because Lincoln was riding from the White House. His hat was shot off and the bullet almost hit his head. The precise location should be updated if known.
Abraham Lincoln /ˈeɪbrəhæm ˈlɪŋkən/ (February 12, 1809 – April 15, 1865) was the 16th President of the United States, serving from March 1861 until his assassination in April 1865. Lincoln successfully led the United States through its greatest constitutional, military, and moral crisis – the American Civil War – preserving the Union. Reared in a poor family on the western frontier, Lincoln was mostly self-educated, and became a country lawyer, a Whig Party leader, Illinois state legislator during the 1830s, and a one-term member of the United States House of Representatives during the 1840s.