"Those courtrooms haven't been used in years."
--Arthur Weasley (OP7)
This level is old and can only be reached by the stairs to the left of the door which leads to the Department of Mysteries on Level Nine (OP7). The courtrooms are accessed along dungeon-like corridors of rough stone are lined with sturdy wooden doors and hard benches (DH13). The walls of the courtroom are dark stone. In the center of the room is a chair covered in chains that stands below rows of high benches on which the Wizengamot sit (OP8).
Harry's disciplinary hearing is originally scheduled to be elsewhere in the Ministry headquarters, but it is abruptly moved to "old Courtroom Ten" and the time is bumped up. Harry and Mr. Weasley learn of this just in time to make it to the correct venue (OP7).
The layout of the Death Chamber one floor up in the Department of Mysteries resembles the layout of the courtrooms on Level Ten (OP34).
The courtroom scenes seen through the pensieve take place in room similar if not identical to Courtroom Ten (OP8) and the courtroom used to interrogate Muggle-borns (DH13), so it seems likely that they are also located on Level Ten.
There must be newer courtrooms elsewhere in the Ministry if the ones on level ten hadn't seen use in years and Harry's hearing was originally supposed to take place somewhere else at the ministry. We are never told where these courtrooms might be, but the Department of Magical Law Enforcement on level two seems the most likely place. -BB
One explanation for why the old and disused level ten courtrooms were used in the persecuting of Muggle-borns could be to allow other legal proceedings to go on as usual without the questioning of Muggle-borns doings one or more of the following: a) backing up all the business people have there, b) being visible to potential critics, c) use dementors without affect other people.