The picture above is from the Harvard Zionist Archive. (if you scroll down you will see it again, reinserted so that the caption can be visible). An apparently doctored version of the same event taken from the Ottoman Archives is below. The location was a mystery at first but then identified by some of the people quoted here.
In fact, you can see the arch when you drive along the Old City Walls, southward past Jaffa Gate, and bear right with the road which then goes over the Kidron Valley to your left and Braichat HaSultan to your right . If you could stop there (you can't unless you are walking) and look at the vista today, you would see Montefiore's windmill. It was there when the picture was taken. So the mystery is, why isn't it in the photo?
As pointed out by several readers (of the Picture a Day site, from where these articles are taken, ed.), the location is the public sabil (public fountain) above the Braichat HaSultan (Sultan's Pool) valley outside of Jerusalem's Old City, on the road between Jerusalem and Bethlehem. The event is the public (re)dedication of the fountain, one of seven built by Suleiman the Magnificent in the 16th century.
This screen capture from Google Maps Street View is very close though: Mishkenot Sha'ananim, the arch of the drinking fountain at the end of Sultan's pool, and the Sephardic synagogue in Yemin Moshe can all be seen in both pictures. I'm not sure why the Montefiore windmill isn't visible in the old picture — either it's behind the flag or it blends into the background.
Unless I'm missing something, I don't see where the picture was doctored: the fancy pediment on top of the drinking fountain looks like a wooden attachment made at the time, not photo-doctoring.
Google Street View picture of the site today. Note the windmill of Yemin Moshe
What's missing in the Ottoman picture? A whole windmill!
Here is the same dedication ceremony before the 114-year-old Ottoman version of "Photoshop" (Harvard, Central Zionist Archives)
Why was the windmill, built for the Jewish community in 1857, removed from the Ottoman picture? Perhaps because the imposing structure overshadowed the fountain.
We thank Martin for this additional view of the fountain (below), taken from the Sultan's Pool. The hand-colored picture is from Chatham University's collection of Jerusalem pictures.
The fountain is in the center of the dam beneath St. Andrew's Church and St. John's Eye Hospital (today the Mt. Zion Hotel)
On the road from Jerusalem to Bethlehem (today's "Hevron Road") Note the fountain on the dam.
(Hand colored. Chatham University)