It’s quite difficult to figure out where this is in Harlem simply because so little is left of the buildings you see in the photo:

The subway entrances tell us that it’s got to be 116th, 125th, 135th, or 145th streets and Lenox. The shadows tell us we’re looking north-west.

Note the streetcar tracks in the foreground and the fire/police call-box in the bottom-right corner.

That fire/police call-box is still there, but there are no streetcar tracks and the subway entrance is much less grand:

The intersection is 125th Street and Lenox, and the only buildings that remain (the CVS/Marshall’s Building has taken over the block front) are the buildings on the north-east corner of Lenox/126th Street, above the Corner Social:

The angle of the whole, is tough to capture, given that the original photo was taken from a rooftop (on the south-east corner of Lenox/125th), but this is the best that Google has to offer:

The Directory

Before phone books (okay, I'm dating myself...) the city had directories of residents, their occupations, business addresses, and home addresses.  The New York Public Library has digitized many of these books and you can use them to look up who lived in your apartment in 1889, say.

https://digitalcollections.nypl.org/collections/new-york-city-directories#/?tab=about

The directories are filled with amazing ads from the time, and give you an interesting insight into occupations.  

You can look at the PDF's or OCRed text of the directories here:

https://github.com/hadro/new-york-city-directories 

Just open one at a time - they are large files - and once it loads, search for your address.  I've found the PDF's to be better to search as the OCR feature is sometimes iffy.  

Searching for "1982 Madison" in the 1880 directory led to this:

George Daily, a broker who worked at 82 Pearl Street in the Financial District, lived at 1982 Madison Avenue.