Poll sucks for not including the classic JL Satellite.
And not distinguishing:
Hall of Justice was on Earth
JL Satellite orbited the Earth.
The Watchtower was stationed on the moon.
The Animated version pictured was a hybrid of the JL Satellite & the Watchtower.
What most are voting for is Satellite-Watchtower
And then in the comic Hall of Justice became teleporting Gateway to the Satellite-Watchtower.
The way they did it in YJ was pretty good, where the Hall of Justice served as the entrance to the Watchtower.
That version (see above) debuted in the comics, in Meltzer's run I believe.
As far as the movie:
The HQ like the character's themselves, needs a story arc.
- They do need to start off on Earth.
- As the makeshift team first forms, in the Secret Sanctuary cave, deep inside the harbor mountain, becomes the first provisional secret HQ
- Leading to the friendly face, very open to humanity - The Hall of Justice
- Leads to rift in the team - Wayne secretly building the secret Satellite, and the misinterpretation of lording over humanity.
- In the end keep terrestrial Hall of Justice entrance but with transport to the new Satellite-Watchtower. ...visible from earth to humanity, symbolically like a lighthouse.
Incorporates all the elements.