The grand hall where court is held is often referred to as the Red Room, it is a large circular room that could easily house thousands comfortably with several hovering platforms though typically there is rarely more than several hundred in this chamber and utilizing localized acoustic fields tone can have a comfortable conversation without having to shout over others.
The chamber has several places to sit and all focus is brought towards the center where the Emperor sits and on a floating platform sits the Dark Council to overlook the chamber, when the Emperor is in the session all guard positions are held by the Imperial Guard, when he is not present security is handled by elite Imperial Stormtroopers.
There are several mobile platforms to sit and lounge and watch and several holoprojectors connected to the global and Imperial holonet for ease of communication with nearly any location in the galaxy.
The Red Room is only open when court is in session, otherwise it is off limits to all but the Dark Council and the Emperor.
Suspicion: Those who are Untested or lower are allowed entry into the People's Tower.