The place where Abraham Lincoln was shot dead. Ford's Theatre, first of all, is indeed Theatre not Theater: what is now the British spelling -re was more widely used in America back then. It is on 10th Street in Washington, DC.
It began as the First Baptist Church of Washington, in 1833, and lasted as such until 1859, when they merged with the Fourth Baptist congregation. It languished until the end of 1861, when John T. Ford leased it as a theatre, which he called "Ford's Athenaeum". The first performance was on 19 March 1862. In December it was gutted by fire, and a new building was reopened under the name of "Ford's New Theatre" on 27 August 1863.
So it was less than two years later that Mr and Mrs Lincoln went to see a performance, on 14 April 1865, of the 1858 play Our American Cousin, by Tom Taylor (1817-1880), a British journalist and prolific playwright, who was editor of Punch magazine from 1874 till his death.
The details of John Wilkes Booth's conspiracy and escape and death are given in great detail under his node, so I'll only mention what pertains to the theatre. He knew John T. Ford and his theatre well, and he knew the play. He got access and cut a suitable hole in the State Box to give him an easy shot, which he accomplished at 10.15 p.m. when the audience were laughing at a line. He used a .44 calibre Derringer.
He leapt from the box onto the stage, crying Sic semper tyrannis, 'Thus always to tyrants!', but tripping on the flag that draped the box, he broke his leg. The broken leg was part of how he was later tracked down. (The story that "Your name will be Mud" comes from the Dr Mudd who treated him is probably an urban myth.)
Ford, having averted having his building destroyed by a mob, sought to reopen it as a theatre in July, but it was taken over by the army (a lease becoming a $100 000 purchase a year later), and converted to a three-storey office building, with the War Department on the bottom floor, the Army Medical Museum on top, and the Library of Medicine in the middle.
From 1887 it was exclusively War Department clerks, 22 of whom were killed in a major collapse in 1893. It was reduced to a warehouse, and transferred between departments, and in 1932 a Lincoln museum was established on one floor, but it was not until 1965 that proper restoration work began.
Helen Hayes was the guest star in a gala inaugural performance on 30 January 1968, and from February 1969 it held regular theatrical performances once more. The theatre and The Petersen House were united under the name of the Ford's Theatre National Historic Site in 1970, having been managed by the National Parks Service since 1932.
And no, as far as anyone knows, the reporters did not ask, "Apart from that, Mrs Lincoln, how did you enjoy the show?"
Their home page: http://www.nps.gov/foth/index2.htm