Locke will start the scenario being chased by an Imperial soldier. His current mission is to find a way out of South Figaro (his original mission here apparently complete), but doing so will not be simple. Your first order of business should be to equip him, because he took off all his current gear when he left in the Returners' Hideout. You likely found a nice upgrade for him in the form of an Air Lancet in addition to his original gear.
You don't have free reign in South Figaro, but Locke is a thief treasure hunter. There are three types of characters in town that you can fight. Merchants are not a threat, but your goal isn't to kill them. Instead, you can Steal a disguise (and a Plumed Hat!) from them, which will give you more options to get around town. The green Officers can be handled in much the same way, giving you an Imperial disguise. However, avoid the soldiers in magitek armor—these will lead to fights with HeavyArmors, which Locke will likely not survive. The good news is that dying just sends you back to the starting point. (If you're overleveled at this point, you can take out the HeavyArmor in the southeast part of town to skip a few steps when exploring.)
With your path outside blocked, you'll have to search the nearby buildings for a path through town. Duncan's wife gives you a hint about a drafty room in the mansion, and you'll find a save point in the basement (which finally has a reason to exist!). The nearby building belongs to an old man who doesn't like strangers, but states that he'll talk to you if you bring him Cider. His grandson won't let you pass unless you're dressed as a merchant, which is an oddly specific phrasing.
Fortunately you can find and rob one such merchant in the Item Shop, along with the usual items for sale. You can steal his clothes, leaving a B.Day Suit in his place, then the old man's grandson will let you pass. All that just to get past one HeavyArmor!. You can find a Tonic in the bucket in the east room downstairs in the old man's house if you didn't grab it earlier.
You now have access to the eastern half of town, including the Weapon and Armor Shops. Neither is selling anything new, but if Locke still needs any upgrades from earlier, now is the time. Soldiers are blocking the entrance to the mansion, and the HeavyArmor in the area will attack even if you're dressed as a merchant, so be careful. (If you are defeated, you'll lose your disguise and have to go through that whole process again.)
With nowhere else to go, head up the stairs east of the Arsenal. Follow the town's outer wall around to the west until you run into a green Officer. As several townspeople will tell you, they love to fight and will attack even a lowly merchant. Steal a disguise to open up some more exploration options. Imperial soldiers will also now speak with you, mentioning an impending invasion of Narshe. You still can't enter the mansion, but HeavyArmors will no longer attack you. Most importantly, the soldier near the crates south of the mansion will now move if you speak to him.
You'll only find one building in the southwest part of town, the Cafe/Inn/Relic Shop. There is an Officer and a HeavyArmor near the entrance to the docks who will attack if you return with a different disguise. Make sure you gather information about various secret passages from the soldiers in the Cafe while still disguised as one of them. You'll find a Merchant in the Inn, but the one you're looking for is in the Cafe Cellar. He'll attack even another merchant. Steal from him to earn not only a disguise, but the Cider as well.
Now you can return to the old man's house (still disguised as a merchant so his grandson will let you through). He'll tell you about a secret password, but can't remember what it is. You'll just have to guess—fortunately there are only three choices. The correct one is "Courage." If you get it wrong, you'll lose your disguise and return to the starting point as if you were defeated in battle. You don't need a disguise to try again, though.
The secret passage leads to the east wing of the mansion. You may have previously explored this area. There is an Elixir in the clock at the mansion end of the passage, and a Fenix Down in the bottom barrel in front of the nearby mansion entrance. You can speak to everyone in the mansion, but the only new information is the little girl's rhyme about winding the clock. The woman complaining about the draft in the South Figaro Mansion 2F West Room is nowhere to be seen, but you can actually hear the draft instead of music in this room. The hidden passage is behind the bookcase on the left side.
The passage leads to a narrow hallway. If you're still wearing a disguise, you'll be given the option to remove it. Celes has a different reaction based on what Locke is wearing. It's fun to get a disguise from an Officer just for the Star Wars reference here. Before proceeding, follow the north-south hallway past the east-west hallway to find a secret basement with two very nice relics: the RunningShoes and Hyper Wrist.
Walking by the first door triggers a cutscene where you are introduced to (and can name) general Celes. Go in and free her, and she'll join the party. She'll also tell you to examine the guard, who is holding the Old Clock-Key you'll need. You'll find a save point behind door number 2, and it would be a good idea to save at this point since dying up ahead will result in an actual game over. You'll find gear for Celes soon, but it makes sense to give her any spare equipment you may have for the moment.
The third room holds four chests and two clocks. The chests contain a total of 3,000 GP (one is empty), while surprisingly neither clock hides an Elixir. The second clock can be wound with the Old Clock-Key, though, revealing a hidden passage to a basement maze.
This is the first part of Locke's scenario that features random battles. You'll meet both Commanders and Vector Pups down here. Both use different tactics when alone: Commanders become more aggressive and powerful, while Vector Pups run away. Neither is vulnerable to Celes's Ice spell specifically, and both take more damage from physical than magic attacks. Vector Pups have more HP and counter normal Fight commands, so you can avoid some pain by taking them out one at a time and letting the last one Escape. (This may be unavoidable when a pair appears without a Commander alongside them.) Relics like the Genji Glove and Hyper Wrist can be helpful here, allowing you to take out foes in a single attack.
The treasures in this area are scattered all over, but they're worth finding because they include a full set of gear for Celes. You'll find Iron Armor south of the first intersection, which should increase her defenses substantially. You can see a trio of chests west of the next intersection, but you'll have to head up and around to reach them. They contain a Heavy Shld and a RegalCutlass.
Back at the second intersection, you'll have to head south through a hidden path. While traversing it, look for a hidden path to the left: this will eventually also turn south, leading a second basement area with amazing treasure: an Ether, an X-Potion, and the always-fantastic Ribbon. The Ribbon is carefully hidden: the chest can't be seen, but it's directly south of the X-Potion behind the wall.
Continuing down the original southern passage, you'll want to head all the way to the end of it and then west to find Earrings, a nice relic for Celes. The nearby path to the east will lead out of town.
Your destination is Narshe, which means heading back through the South Figaro Cave. You'll probably want to rest up, though. You can save the cost of a Tent or Sleeping Bags by heading to Duncan's Cabin to rest for free. The monsters in this area aren't very threatening, but you do only have two party members at the moment.