Hiding in Plain Sight
Tossing and turning in your semi-consciousness, you dream of a female Jedi wielding a yellow lightsaber in heated combat with a Sith. As you awaken, you find yourself in a one-room apartment with Carth staring expectantly at you. This is a chance for Carth to provide a little exposition and fill you in on what needs to be done. It seems Bastila's escape pod may have crashed somewhere in Taris's Undercity and it's up to Carth and you to search for her. Who's going to be looking for a couple of regular soldiers anyway, right?
The tiny apartment will serve as your base as long as you're stuck on Taris. On the back wall is a footlocker that not only has a few medpacs, but may also be used to store items you don't want to carry with you. There's also a workbench along the back wall where some armor and weapons can be upgraded (assuming you have the necessary upgrade parts). You can use this opportunity to talk to Carth a bit and get to know him better. When you're ready to set out, head toward the door. Since Carth is the only other party member you have, you'll have to take him with you.
Home, Sweet Home
As soon as you leave your apartment, you'll stumble upon a small Sith patrol harassing some of the non-human residents. After murdering one of the Duros, the Sith will recognize you as "Republic fugitives" and attack. Attack either one of the droids, having Carth target and attack the same one. Once both of the droids have been dispatched, eliminate the human Sith and collect the items left on his person. Thanks to the surviving alien (who kindly offers to "reinterpret" the scene of your tussle), you won't have to worry about discovery by the Sith...for now.
With that little scene over, you should be free to move around the building as you please. Just a few steps from where your fight took place is a green-skinned Twi'lek named Larrim. Walk past him and he'll try to see if you're interested in any military-grade energy shields. While his shop is quite convenient, it may be wiser to hold off on any purchases as Larrim's goods can be considerably pricier than other local stores. You can also explore the apartments of your brand new neighbors and do what any good neighbor would do...loot some stuff. In total, there's Republic Credits43, 4 repair parts, 2 computer spikes, and 2 medpacs to be had. Once your done exploring, head down the elevator and out into the Upper City.
The Sith Occupation
There's a fair amount to see and do here in Taris's Upper City. In order to find Bastilla, you'll need to get down to the planet's lower levels. The only way to do that is to get past an elevator guarded by the Sith. Since getting the requisite authorization papers is highly unlikely, you'll need a disguise if you want to get past the guard.
Heading south from your apartments (straight ahead) you'll find the Equipment Emporium, a shop operated by Kebla Yurt that sells weapons, armor, and medpacs. Stop buy and purchase some equipment if you need it. Just before reaching the Emporium though, you will be given the chance to chat with Carth and get to know him a bit better. Continuing on, you'll come across the Upper City Cantina. In the cantina's first room are a couple of pazaak players. You'll need a deck if you want to play but it can be a quick way to earn some cash.
If you're looking to get your disguise without a fight, the cantina will be the place to go. If you're playing as a male character look for a Sith officer by the name of Sarna, if playing as a female look for Yun Genda. Whichever one you talk to, just chat the officer up and try to get on his/her good side, make them believe you're sympathetic to what they're going through. If you succeed you should get an invite to a party some of the officers are going to have after their shift is done. With the invite secured, feel free to explore the cantina.
The first room to the right of the entrance features little more than a stage with a few dancers and musicians performing. The next room around the perimeter (moving counter-clockwise) is the bar. There's not much to see here except for a spoiled rotten brat named Gana Lavin. If you speak with her she will get pissed, no matter what you say to her. This will result in her bringing two fairly weak thugs to ambush you near the entrance to the Equipment Emporium when you next go by there. The thugs carry little more than a few credits and some low-powered weapons. If you're looking to avoid any unnecessary violence, ignore her entirely.
The last room here is the lobby for the Duel Ring. Here you can engage in duels for money against duelists who become more difficult with each match. While you can probably defeat the first one or two opponents with ease right now, you may want to come back after gaining a few levels before beginning to challenge the tougher opponents. There are five total opponents you can fight against for a total of Republic Credits1500. You may also fight with Bendak Starkiller (the man clad in the yellow Mandalorian armor near the cantina entrance) after you have defeated Twitch, though this fight is best saved for later. Inside the lobby is a storage container containing a single medpac, just in case you take more damage than you like.