Location of the droid:
- Go to the Imperial Fleet
- Go to the Mission Departures elevator ("West" elevator, or far left elevator on the Imperial Fleet Map - the elevator icon should be green if you have the quest)
- Select Interfleet Transport option on the elevator button
- Go into the Shuttle Bay and take the taxi to the "Zoist Shadow Shuttle" (top transport fleet - oooh and ahhh at the impressive Imperial Fleet)
- Once at the Zoist Shadow Shuttle, go to the elevator and select "Zoist Shadow Mission Deck" (should have quest icon/triangle)
- When you come out of the elevator shaft (heh heh...I said shaft), turn RIGHT, then TWO IMMEDIATE LEFTS and you'll be at the entrance into the mission area. MUST BE IN AN OPS GROUP in order to go into this area.
I haven't made it past that part, but I'm assuming the droid will be inside the hanger as the quest instructs. Just need to get a group to do the quest.