evelynnesbit

en.wikipedia.org/wiki/Harry_Kendall_Thaw

Actually, not the courthouse, but instead the photo was taken in front of the Ludlow Street Jail, no longer standing. The sign by the front door reads "New York County Jail" (New York County is essentially Manhattan), and that is what the Ludlow Street Jail was.
Thaw, in 1915, was returned to New York City after escaping confinement at Matteawan State Hospital (He had been acquitted of the 1906 murder of architect Stanford White by reason of insanity). His lawyers successfully asked the court to move him from The Tombs to the Ludlow Street Jail, on the basis that he was not charged in a criminal matter, but that he was to have a jury trial only as to his present sanity.
query.nytimes.com/gst/abstract.html?res=F10916F93E5D16738...
In this old print, you can see that the door was near the corner of Ludlow and Essex Market Place. [Essex Market Place ran from Essex to Ludlow Streets between Broome and Grand Streets and was closed in 1926, around the time the jail was demolished.] You can see that there was a giant gas lamp over the door, whereas in Bain's 1915 picture just the bracket remained.
digitalgallery.nypl.org/nypldigital/dgkeysearchdetail.cfm...

knickerbockervillage.blogspot.com/2009/10/seward-park-aer...

This was probably taken when Thaw was due to be taken from the jail to court.
He and 5 others who helped him escape the state hospital were tried in March, 1915 and acquitted. He then had a second trial in 1915 to determine if he was presently sane. He was determined sane in this trial on July 14, 1915, which is presumably about when this shot was taken.
The New York Times account describes 2,000 people gathered at the courthouse, cheering thaw after the trial:
query.nytimes.com/gst/abstract.html?res=FA0E10FC3E5A15738...

See also:

And not to forget, the Thaw trials were about Evelyn Nesbit Thaw, or more exactly Thaw's shooting of her presumed lover, Stanford White.

Wow! Great photo.

Repeat appearance: Evelyn Nesbit (December 25, 1884 – January 17, 1967) was an American artists' model and chorus girl, noted for her entanglement in the murder of her ex-lover, architect Stanford White, by her first husband, Harry Kendall Thaw. This was likely taken at her husband's trial. Evelyn & son:

I think that the photo was taken aboard a ship, probably (since it is a Bain Agency photo) a ship in New York harbor. In 1914, Evelyn Nesbit Thaw announced her conversion to the Catholic faith, appeared as the star in a silent film, "Threads of Destiny," and published the first version of her autobiography, under the title, "Story of My Life." Any one of those events was sufficient to keep her name in the news.