Captain Marvel was similar to Superman in many ways, but his stories seemed to be more of a little kid - type fantasy than those of the Man of Steel. And rather than simply being a secret identity, Billy Batson appears to be a completely different individual who switches place with Captain Marvel, who shares the powers of various characters from ancient history and mythology, and can be seen as a sort of a guardian angel.
The "Hall of Shazam" was where Billy Batson had originally found the old wizard Shazam, who gave him the combined powers of the six ancients. Billy would go there every now and then to contact the old wizard. The implication was that the tunnel had been built by the ancients, although it appeared to be located somewhere in New York city and was ordinarily taken to be a subway tunnel. I don't know how often they had the sign that said "The Hall Of Shazam", but the sign with the first letter of the six names spelling out "Shazam" was a recurring thing in these stories.
In this story, we get to see not only the ancient wizard Shazam, but Solomon, Hercules, Atlas, Zeus, Achilles, and Mercury as well. Ordinarily they merely lent Captain Marvel their powers from offstage, rather than participating in the action themselves.
Captain Marvel Shazam Page: