Finding Tower of Babil
Once outside, go to the left of the door and head along the coast as far as possible. Now head straight up (ignoring all splits in the road and continuing north) until you can see some tanks. Head to the right side of the tanks. The tanks will attack the tower, allowing you to get through.
Tower Of Babil (B13)
Inside the tower head straight through and immediately head left to find a chest with Ice Arrows x10, then head south to find another chest with Ice Arrows x10. Go back and to the right, wrapping around the path to find a chest with an Ether. Proceed north into the door ahead of you.
In the next room, picking up a Green Beret from the chest west of you along the way, follow the path until you get to the first door you come to. Go inside, and open the chest, guarded by a Alert, which rewards you with an Icebrand after. This will be important for fighting Rubicante. Continue on to the door above you to the right. There will be another chest guarded by a Alert, which will contain the Ice Lance. Continue on to the only other door in the room.
B11 & B10 (Secret Area)
Immediately head left and pick up the Cat Claws, then start to follow the path around the room. Go right and south at the first fork to find a chest containing Phoenix Down, and a door up to to B10. Enter the door and open the chest to the left for a Killer Bow, then head to the right and open the chest for an Antarctic Wind before returning to B11. Take the first path north available and open the chest at the end of the next fork for a Hi-Potion. Continue all the way around until you reach the next door.
B10 (Main Area)
The door directly left is a save point. Use the opportunity to save your game and continue across the first bridge, heading south to find two doors. The door on the right leads to an empty room, but the door on the left contains a guarded chest, with a Alert and an Ice Armor. Head north to find another room with a Alert and an Ice Shield. Continue across the second bridge and into the final door.
B9 & B8 (First Area)
In the next room, go all the way to the bottom, take the north path to find a chest with Arctic Wind, and then continue all the way to the right, take the right path to find a Hi-Potion, and then all the way up to the next door (the path with the bridge is blocked until later). When in the next room, there is only one door to enter, so go through it.
In this room there are two paths on the right. If you take the top path you will get to a save point. The bottom path will take you forward in the tower. The chest along the way contains a Dry Ether.
Continue on to the middle of the room where you will see Dr. Lugae speaking with Rubicante.
Boss: Dr. Lugae
After some dialogue, Dr. Lugae will attack the party. You'll be faced against the doctor and his robot. Depending on who you kill first, this fight will go one of two ways.
Option 1: Balnab, Balnab-Z, Lugaborg.
If you defeat Balnab first, Balnab-Z will show up and you can get his entry, then once you defeat it, a more powerful Lugaborg will show up.
Option 2: Dr.Lugae, Balnab, Lugaborg.
If you defeat Dr.Lugae first, Balnab will blow itself up and likely kill one party member, at which point a more powerful Lugaborg will show up.
Alternatively, if you use Rydia's Titan summon twice, and have everyone else go all-out attacking, you should be able to defeat the doctor and the robot around roughly the same time, skipping the self-destruct altogether, and going directly to the second fight with a full party.
In the first fight Dr.Lugae will command the robot to attack, and it will first attack him, before he commands it more clearly to attack you. Regardless of who you choose to kill first, just hit them with attacks. Either way; once the fight is over, the doctor will turn into a new boss for you to fight. In his new form, he mostly prefers to drown the party in sleep and poison status effects. Don't worry about healing them off, they're applied too quickly to matter, and he will occasionally use Restore anyways to cure all debuffs on your party. Focus on simply pounding him into nothingness with whoever isn't asleep, and try to keep everyone healed in case he uses Laser or Beam. Winning the fight gives you Lugae's Key.
Return to B9
Backtrack down several levels until you reach B9, and go up the bridge you skipped earlier, leading to a locked door. Use the key on this door, and you can get inside to stop the Cannon. After a simple battle with Dark Imp x3, Yang will sacrifice himself to stop the cannon. You won't be able to Warp or Teleport out of the tower, so backtrack on foot all the way to the entrance.
Saved By Cid
When you are about to exit the tower, Golbez tries to kill you, but Cid saves you with his airship. Once you are in his ship, he will jump out of the ship holding a bomb, blowing it up and sealing the entrance to the underground, letting you escape. He tells you to return to Baron and speak to his engineers.
In order to reach Eblan, your next destination, you must use the hovercraft. Go into Baron Castle, and go down the stair case on the right. When you find yourself on the interior of the castle, speak to the engineers who will adjust the aircraft for you. Using the new airship, locate the hovercraft, which probably is still at Mt. Hobs. Position the airship above it and press the action button to pick it up.