The main story would deal with a strange suicide in a town such as San Francisco in the 30s. The latest case deals with the disappearance of a mother and her child.
Each time the bodies are severely damaged, leaving little information for identification and clues for the case.
The characters would pursue their investigation, which in the end reveals the presence of a monster in the town. The monster's presence is kept a secret by the chief of police who moves the body each time to a particular location.
Now the question, which location serves this purpose ?
I thought maybe a railway but drivers could be questioned even if they move town every day. By the seaside, which would feed the Cthulhu atmosphere, but it doesn't explain the mutilation.
Bonus point: if you can build a terrifying location known by all inhabitants of the town (bridge of despairs...)
The police chief is a member of the cult, he might prefer the most credible approach.