What I've searched through the White Gold Tower indicates that Uriel and probably all emperors, did not have a room. Room for the Battlemage, guards, moth priests and the Elder Scrolls library. Any explainations?
The battlemages chambers was probably for the Imperial Battlemage, maybe the Emperors room was hidden away behind a trap door magical barrier or could only be entered using a portal (like the Arch-Mages quarters in the university) or some sort of teleportation. But who knows.