A projector on the shiny little droid lights up, and a three-dimensional display of the station appear. This place is HUGE.
A red blinker appears in a docking bay. Another one appears, near the north pole of the station. A red patch then winds it's way through the station. As the station is still under construction, many areas are exposed to hard vacuum, so the path connecting the two dots is very twisty and convoluted. The path also avoids checkpoints and the like. There's a few blast doors to get through - you'll cross through three different sections of the station - but most of the corridors should be low-traffic.
The station is divided into 12 slices, and two hemispheres, making 24 total sectors. You are in sector 8. The detention area is about twenty decks above you. The trouble Galen was making started in section 4.
The route takes you towards the core of the station, where you'll use some service lifts to get up a few decks. More travel, then another lift. Finally, a bit of a climb, and you'll be in the detention area. From there, it's not far to the throne room. It's probably an hour worth of travel, barring any interruption.