Objectives: Make contact with Gadon Thek, leader of the Hidden Beks
Welcome to the frying pan. Remember the content citizens of the Upper City? The polite protocol droids, eager to help? Well, in the Lower City, you're not likely to stumble across any happy citizens--though you may trip over a corpse or two. This is gang-controlled turf, and as soon as you walk out of the elevator, you'll find yourself caught up in a gang war. You don't wind up fighting for your life because you're a human, or because you're from another planet, or because you ask the wrong questions about a missing Jedi, but because some Weequay foot soldier decides that you're a "stranger." That sounds ironically xenophobic coming from an alien from outer space, doesn't it?
Anyway, the first battle pits you against three fighters from the Black Vulkars Gang. Depending on your class, this fight can be quite tough, so keep your medpacs handy--it's probably a good idea to pause every couple of seconds to make sure your health is full. When you unpause the game, try to run back a ways towards the elevator to disperse the crowd. Pause as soon as the aliens come around the corner, and open fire on whichever of the three aliens took the most damage in the gang fight. If you're a melee character, this may be a good time to attempt an active combat feat like flurry on the first enemy, to close within range; these guys don't have much defense, but can overwhelm a fairly strong fighter if they manage to surround you. Keep pausing and making sure that you and Carth are attacking the same enemy, and you'll get them eventually. If you die repeatedly, try catching them off-guard with a grenade before they can chase you.
As in the Upper City, there are plenty of places to go and see down here, but in order to progress in your quest to find Bastila, you'll need to hook up with the "nice" gang leader, Gadon Thek of the Hidden Beks. Take a left from the entrance and head northwest; you'll come to the entrance to the Hidden Bek base without incident. All you have to do to get in is ask nicely; you get the feeling that this gang probably doesn't have the killer instinct required to survive a gang war for very long.
After walking around inside, you encounter Gadon and his bodyguard Zaerdra. Gadon knows where Bastila is, and is willing to help you find her, but first, you must help him out by finding an accelerator for a swoop bike that was stolen by the Vulkars. You'll eventually need to trade him your Sith uniform for a set of Sith papers that will allow you access to the Undercity, since he believes that a Twi'lek named Mission Vao will help you get the accelerator. With papers in hand, you can head further on to the northwest to reach the Undercity elevator, or you can fool around in the Lower City collecting items and experience, if you wish.