The eastern exit from Mt. Kolts spills into a narrow strip that leads to the Returners' Hideout to the north. The enemies here are the same as those found in the South Figaro Area, though they appear in different combinations. You've gained some levels and new gear since you last fought them, not to mention a new party member in Sabin, so they shouldn't pose any problem.
The Returners' Hideout
Upon entering the Returners' Hideout, you will be escorted to a meeting with Banon. After a rather intense confrontation, you will wake up controlling Terra. In order to advance the plot, you'll need to find and speak to all of your party members. You should take advantage of this time to explore and gather the treasures to be found here.
The Bedroom you start in is where you'll find Locke and a Fenix Down. It exits to the Main Cavern. You'll find Sabin near the Item Shop counter to the south. There are no new Items for sale here, though you can pick up Sprint Shoes in addition to basic Items. There's a Green Cherry hidden in the pot a bit to the north, as well as an unseen scrap of paper on the table. If you investigate the top right square of the main table, Terra can choose to throw it away or leave it there. Leaving it there triggers an inconsequential extra bit in a coming scene.
You'll find Edgar, a save point, and a Potion in the room where you initially met Banon. South of the Item Shop, you'll find the inn, which is free. Despite having been asleep, your HP and MP weren't restored earlier. Sleeping here now will only restore Terra, so it may be wiser to wait until the party is gathered together again.
You don't need to explore the northern part of the Returners' Hideout, but it's where you'll find the best treasures. The visible chests contain an Air Lancet, a Fenix Down, and a True Knight Relic. You can also find an Antidote and a Tincture in the bucket and pot at the north end of the cave. You're not done yet, though! From the north, head right around the pile of crates and look for a hidden passage in the wall. This leads to a White Cape that protects against Imp and Mute and offers a nice defensive boost.
Once you've gathered the treasures you want, return to the entrance and speak to the guard. He will indicate that Banon is waiting for you outside. He'll ask Terra to be a shining ray of hope. You have the option of saying yes or no. However, if you do say no, you'll have to speak to Banon again. Saying no three times gets you a Genji Glove and replaces the upcoming meeting scene with a short bit of introspection from Terra. Saying yes earns you a Gauntlet instead. The Genji Glove is not as great as it may seem (simply because attacking with weapons is so underpowered in FFVI), but the Gauntlet is still the weaker choice. Either way, the most likely candidate for their use in the immediate future is Sabin (though you may not actually have a second weapon for him to equip yet).
If you don't like denying Banon that much (or just want to see the meeting scene) but still want a Genji Glove, you have another option. After saying no at least once, return to the Northern Cavern and speak to the guard there. He will give you the Genji Glove, and Banon will no longer give you the Gauntlet even if you go back to him and say yes after all.
After agreeing to be Banon's ray of hope, there will be a strategy meeting. It will eventually be interrupted by the news that the Empire has invaded South Figaro. If you denied Banon, this news will arrive after your third no instead. Either way, Locke leaves the party (and his gear), replaced by Banon. He is a temporary character like (most of) the Moogles earlier in the game, so you can't change his equipment.
At this point you'll find yourself at the north end of a narrow hallway. The door behind you leads back to Banon's Room. You can head back and save and stay at the inn to recover your party if you haven't already before proceeding onwards.