If you're talking about the so-called Lincoln Conspirators (Mary Surratt, Adzerot, Herold, Powell/Payne, etc.), it was in the yard of the Old Capitol Prison.
Edit - Although at least one of the Lincoln conspirators (Mrs. Surratt) was temporarily held at the Old Capitol Prison, she and the others were hanged in the courtyard of the Washington Arsenal Penitentiary, which was not the same place as the Old Capitol Prison.
Hoosier