After much sleuthing, including trying to get the right perspective using old DC maps, I can positively identify the large white building in the upper right as being the “old” Providence Hospital located at the time at 2nd & D Streets SE on Capitol Hill (see the image in the plaque below).

I’m a bit embarrassed it took me so long to figure it out--I was born there in 1950. Dating to the Civil War era, the hospital moved in the 1950s to larger quarters in Northeast. The buildings in the photo were razed and site became Providence Park, which still exists today. Incidentally, a number of previously published Shorpy photos were taken around the same time frame from the roof of the hospital, including several pointed back in the general direction of the Randall School—the reverse of where we’re looking from in the photo above.

The prominent group of structures at 2 o'clock is the old Providence Hospital complex. It's a park now.

Goats of Venus has indeed got it right. [As does the photo caption, which calls it a coal yard - Dave] A look at a 1904 Sanborn Fire Insurance map shows this to be the Allegheny Coal Co. The map clearly shows the hard and soft coal trestles as well as the other structures on the site. Even more fascinating, it matches up perfectly with the houses in the image (facing H Street) and accurately shows their construction, with the pink color representing brick and yellow being frame. Even the 2-story frame porch on the house in the foreground is shown on the map as well as the split brick and frame construction of the first house around the corner on Half Street.

I'm curious about the complex of large white (at least in this picture) buildings in the upper right. Can we identify that?

I believe we're looking at a coal dealer. Note that some of the bays are divided so the coal can be sorted as to lump size and possibly some choice Anthracite in there.
Seems to be a small cart-ramp extending over yet more bays below.

The elevated rail arrangement and piles of ballast in the center-right of the photo remind me of all the comments and speculations last week with regard to Earth Movers: 1901.

The partially visible large building in the upper left of the image is southeast corner of the Jefferson Building of the Library of Congress, which was completed four years before the image was taken.

Flags are flown at half mast aboard ships. On land they are flown at half staff.

Is that the Library of Congress in the distance on the left?

When he died President McKinley was widely and deeply mourned. The trappings of official and Victorian mourning with black crape and formal mourning attire were everywhere. But so also were touching demonstrations by simple people throughout the country where public assemblies and special services in churches were held. The route of his funeral train was lined by ordinary working class people standing shoulder to shoulder with the well off and powerful. People placed coins and flowers on the train tracks and kept the flattened remnants as mementos. At almost every stage of the journey local bands appeared playing the hymn "Nearer My God to Thee," a popular hymn and Mr. McKinley's favorite long before it became associated with the Titanic disaster. McKinley was a deeply religious man and according to popular legend (disputed) his last words were from the opening verse of the hymn.

Here is a link to some rare film footage of the official ceremonies and funeral procession. https://youtu.be/gTQrpsZ3tQA

I had always assumed that the little turrets, or cones on the corners of houses were purely for appearance. I wonder whether they also played a structural purpose since more than two dozen of them are visible in the picture.

Elsewhere in the city, "that damned cowboy" Teddy Roosevelt has just become the new President.

I was 7 when President Kennedy died. I never hear mention of Dallas without thinking of his assassination. I've always wondered, did people who were alive when McKinley died have similar associations with Buffalo, where he was assassinated?

The assassination of William McKinley made Theodore Roosevelt President at the age of 42. When TR became Vice President earlier that same year, his friend Charles G. Washburn remarked: "I would not like to be in McKinley's shoes. He has a man of destiny behind him."

Such a stark contrast exists between the pretty house with delicate embellishments casting lacy shadows -- the two older folk porch sitting on an early autumn afternoon; the younger woman dressed like an Old West frontier female standing by, arms crossed; the hatted child playing at the edge of the sidewalk -- and the rest of the landscape, which appears suspended in a dusty, lonely languor.