This is the Jefferson Market branch of the New York Public Library. Originally (1877) it was a courthouse/prison/market. The architecture is supposed to be Neuschwanstein-ish. And since it’s a public library, they let anyone inside! Like me!
It was recently reopened after a three-year, $10 million renovation. This is the adult reading room on the second floor (it used to be the civil court).
The children’s reading room is on the first floor, and the reference room is in the basement (and used to be a holding area for pre-trial prisoners). At one time (1958) there was talk of demolishing it, but the public complained, and now it’s a protected landmark.