Spectators at the Capitol for the Grand Review
Spectators at side of the Capitol, which is hung with crepe and has flag at half-mast during the Grand Review of the Union Army, May 23-24, 1865. The signboard at lower center reads, “WELCOME BRAVE SOLDIERS.” Viewers of the film Lincoln may have noted that the Capitol’s iron dome was shown in the movie as a dark gray, instead of painted white as it is now; this can be seen at the top of the image. Based on the shadows, I’d say this is the north end of the Capitol, looking south. Library of Congress. Larger version here.
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Dead Confederates, A Civil War Era Blog 
The slope of the ground supports your hunch about where this is.
Thanks.
The flag to the right of the dome appears to be at half-mast. I suppose that might be for Lincoln, even though he had died more than a month earlier.
The black crepe, too. The official mourning period for a president now is 30 days, but I don’t know there were any rules or tradition then.