Medivh's Chambers, located near the summit of Karazhan, are the private bedchambers and study of the last Guardian of Tirisfal. The room contains a worktable, an elevated bed, and many paintings and statues.
To enter Medivh's Chambers, it's recommended that Karazhan be cleared first, as there are several fleshbeasts within the room. There are two entrances; the first, which appears to be the "front door", is just outside the Gamesman's Hall on the way to Prince Malchezaar. Leave the Gamesman's Hall and enter the doorway to the left, and up the ramp to the door. The second entrance, which appears to be the "back door", is halfway up the staircase to the tower summit.