The imperial capital of Vector is unlike the occupied towns on the southern continent. This is the heart of the Empire's power, and it sports a unique, harsh look to make that clear. You are not welcome here, and the northern half of the town is filled with patrolling soldiers that will attack if they find you. Fortunately, you don't need to venture into the dangerous parts of town to find a path to your immediate destination, the MagiTek Factory.
Shops and Inns
There is nothing in the Vector shops that can't also be purchased in Albrook. The Armor Shop is identical, and the Weapon Shop has a smaller selection than the one in Albrook. There is no item shop to be found here at all. There is an Inn, and while it is technically free, you probably do not want to stay there. There's a 50/50 shot you'll be robbed of 1,000 GP each time you do. Fortunately, there is another option. Head west to the small Hut where you'll find an old lady asking if you pledge allegiance to the Empire. Nothing happens if you do, but if you refuse you'll be accosted by a pair of Guards. These are the same ones you remember from Narshe, and offer absolutely no threat. Once defeated, the old lady will heal you for free any time you return from now on.
There is no Treasure to be found in Vector, but a few of the townspeople have interesting things to say. One lady tells you that Cid gave her child the power of Cure magic. The child can indeed heal you, but only for 1 HP each time you speak to him. The customers in the Cafe on the west side of the upper level share several interesting tidbits, including that Kefka was Cid's first experiment and while he was given the gift of Magic, his mind snapped as a result. Just be careful heading to the Cafe as the nearby guards are hostile.
All the guards in the northern part of town are hostile, and any battle with one will end with the party retreating to the entrance of Vector. There isn't a lot to be gained by fighting here, especially since you will have to walk back to the hostile area after each fight. Normal soldiers take the form of two Garms and one or two Commandos. Both have moderate HP totals but a high resistance to physical damage. Magic or magical attacks are your best bet, particularly Thunder-based ones. (Water also works well but only Gau can take full advantage of that weakness at this point.) The last Monster standing will use a "Program" special attack that causes a Status: Muddled for Garms or Mute for Commandos. I'd recommend taking out the Commandos first since their Status lasts past the end of battle.
The soldiers in MagiTek armor represent an encounter with ProtoArmors, sometimes in pairs but usually accompanied by 2 Pipsqueaks. The Pipsqueaks can turn your Characters into Imps, but have low HP and are vulnerable to Thunder and other Magic. Try to take them out quickly. ProtoArmors will sometimes use Schiller if they are alone, but the Dark Status it inflicts is no problem. Both of these Monsters will counter uses of Fight with nasty attacks, so avoid doing that. As with the other monsters here, these are highly resistant to physical damage. They also all share the weakness to Thunder.
The Guardian
If you manage to maneuver past all the guards through the north exit of Vector, you'll find yourself at the entrance to the Imperial Palace. You'll be spotted if you try to enter, and attacked by the Guardian if you try to leave. As the man in Tzen advised, you should run away from this foe. Its attacks are fairly powerful, though only made in response to your own, but the Guardian is utterly invincible. Running is the only option. You'll find yourself at the north end of Vector if you do run. You'll have to fight the Guardian again if you re-enter the Imperial Palace.
The Returner Sympathizer
When you're ready to head to the MagiTek Factory, look for the old man behind a pair of crates in the southeastern part of town. He's a Returner sympathizer, and will fake an illness as a distraction to allow you to pass. Climb onto the left crate, then you'll automatically follow the girders east and jump down onto the train track path. Follow the tracks north until the path forks. This is the entrance to the MagiTek Factory. Note that if you head back towards town, the guards will attack you just like the wandering guards in the northern part of town, and you'll need to talk to the sympathizer again to proceed. If you need to leave the MagiTek Factory, you can head down and confront the guards to get the city entrance.