The Returners, led by Celes and Locke, are off to the Imperial capital of Vector to save captured espers from a grim fate: the slow theft of their powers in a Magitek Research Facility. Vector is hardly an inviting area, and the Returners couldn't be visiting a worse place for their kind, but they don't have much choice…
Vector is located in the centre of the continent, and the moment you step inside its boundaries you'll realize it's rather dangerous. The two halves of Vector are a bit different from one another in terms of travel; we'll start with the south.
At first glance the Inn seems like a fantastic deal: free! Don't have to spend a cent. Stay here, though, and you stand a good chance of the proprietor robbing you in the night. There's another way to regenerate your HP, so don't bother with the Inn.
To the east of the Inn is a conspicuously-small home with a single person inside. Talk to her and admit that you are not loyal to the Empire and she'll call two Guards to attack you. Beat them and she'll reveal her try loyalties, to a point, and heal your wounds whenever you talk to her for free. Take that, stupid Inn.
If you visited the other towns on the continent, the Weapon Shop will have nothing of value to you.
The same goes for the Armor Shop, sadly.
The north of Vector has no items or shops, and if you go up here you'll find the whole area patrolled by Imperial troops. Get caught by one and you'll face a fight and a quick flight back to the entrance. Talk to the normal people outside and in the Pub to learn some juicy tidbits of information about the Empire's generals, notably Kefka. Turns out his looniness was accidentally imposed on him. Poor madman. You can go all the way north to the Imperial Palace, but you'll confront a horrifying Magitek weapon called the Guardian which you cannot hope to defeat. Run immediately if you get caught in this battle.
Check the east side of Vector's southern district. You'll see an old man hiding behind a box. Talk to him to learn that he's a Returner who wants to help you. He'll distract the guards while you hop on the boxes and enter the Magitek Research Facility. Don't talk to the soldiers after you've gotten across or you'll face a fight and have to do the box thing all over again.
Follow the tracks and you'll find your way to the Magitek Research Facility's front door, the Magitek Factory. Be warned! The enemies past here are quite resistant of physical attacks, and only special attacks (Tools, Blitz, Bushido and some Rages) or magic will have a strong effect on enemies. If you're lacking in special attacks, or haven’t bothered learning magic, you'll have trouble getting through.