For the many headquarters of the Justice League and Society of America, none was more non-traditional than their penthouse hotel suites which they met at for brief periods.
The Justice League turned to such a base of operations after the Secret Sanctuary had been discovered by the Joker, and after their satellite had been virtually destroyed by a Martian invasion. After dissolving and reconstituting the League into a tighter, full-time band of heroes, Aquaman resorted to this locale until Steel offered the Bunker of his grandfather's Hank Heywood Senior (originally of Earth-Two) in Detroit to house the team.
This facility had several levels beneath the factory, which served as a front for this locale. Containing state-of-the-art defenses and workout facilities as well as living facilities for the Leaguers that resided there. Young mutant heroes such as Vibe and Gypsy from the surrounding neighborhoods were drawn into the team and joined as a result.
The Justice Society actually first conducted meetings for its first several months of existence in a penthouse suite reserved by Wesley Dodds aka the Sandman. This headquarters was also utilized by the initial grouping of the All-Star Squadron before they moved to the Perisphere. Unfortunately, several villains attacked this seemingly secret sanctum including Sandman's old foe Fairytales Fenton, Nazi agents and the Monster Society of Evil (who used it for their own base temporarily, similar to the Injustice Gang on Earth-One using the JLA's Sanctuary).
Then the team moved to Civic City, first to rent a room which was discovered by a curious detective then their own building. It was here that the original Black Canary originally tracked the Society's whereabouts, trailing her friend Johnny Thunder, eventually joining the group in his place.
With their own staff, such as Dale Gunn who maintained the JLA Bunker and Mrs Campion who cleaned up the JSA's Civic City center, the heroes could concentrate on the business of keeping law and order maintained.. not just in Detroit and Civic City and New York City... but around the world as well!