Typically, a Gothic setting is in that of a castle. While a castle is not always necessary, the atmosphere of a Gothic text is always mysterious ans suspenseful.
That said, the Gothic setting of The Strange Case of Dr. Jekyll and Mr. Hyde is one which takes place in London. Although not in a castle, like many Gothic texts, the setting her is more important based upon how the characters feel in the setting which they are in. The characters do not have to be in a castle to feel anxious, instead, the block of Soho is sinister in its own right.
In the opening of the novel, the setting is openly described as mysterious and worrisome:
Certain sinister block of building [which] bore in every feature, the marks of prolonged and sordid negligence.
Here, the buildings which surrounded the men are frightening enough to appeal to the Gothic nature of the story. Following the description of the buildings, Mr. Enfield tells Jekyll about a time he witnessed a man literally run over a little girl while walking.
Through these two descriptions, the reader can come to assume that a dark side of London is being used as the backdrop to the story. Therefore, the setting's dark, mysterious, and suspenseful nature is Gothic.
Although the streets of London and Soho where Mr. Hyde pursues his evil business recall the dark and seedy strains of the Gothic, the primary Gothic setting in the story must be Dr. Jekyll's laboratory building. A Gothic setting is often an old, decaying edifice, perhaps empty except for the supernatural creatures that haunt it, or a secret, forbidden wing or room in an occupied building. Jekyll's laboratory is a separate wing or building from his main home, and it is accessed through a courtyard. Stevenson foreshadows the final scene of the story when Utterson and Enfield, on their "usual walk," take the "back way to Dr. Jekyll's." There, standing in the "premature twilight" of the courtyard, they see Dr. Jekyll in an upper window. After a short, depressing conversation with him, they see his face change to an "expression of ... abject terror," and he slams the window down.
Later, when Poole comes to get Utterson, they make their way into the laboratory building. Its surgical theater is piled high with crates and bottles. There is a stairway leading to the locked "cabinet," a room from which agitated pacing, screams, and cries have been issuing for days. Poole has been leaving meals outside the door, and they are smuggled in when no one is looking. Orders for strange drugs appeared for Poole to fill. One day Poole found a disfigured dwarf digging among the crates; the "masked thing like a monkey" ran away from the chemicals up the stairs and locked himself in the cabinet.
Poole and Utterson proceed to break down the door with an ax; they find Edward Hyde's body twitching from the last throes of death. They then explore the rest of the laboratory building, looking for the body of Jekyll. There are empty closets filled with dust and cobwebs and a spacious cellar filled with ancient "crazy lumber." A "perfect mat of cobweb" falls when they open the sealed entrance. They go back to the cabinet and analyze its contents, trying to figure out the mystery.
Stevenson's presentation of the laboratory as a Gothic setting enhances the "strange case" that Utterson must solve.