Once you've retrieved T3-M4 from the droid shop, use him to open the doors to the Sith base. At that point, you may then want to expel him from your party unless you really need his computer slicing ability inside. Considering the nastiness of the "boss" fight coming up, a different party member may be preferable. However, keep in mind that you will need some Computer Use skill in your group or a whole heap of computer spikes.

Sith Base

1. Exit to Upper City
2. Reception. You may be able to Persuade/bribe the receptionist to not sound the alarm. Otherwise, she'll summon a Sith officer and some soldiers from the room off to the side. You can use her desk to slice the base's security systems.
3. Prison block. A Duros in once of the holding cells is the one from outside your apartment. He's scheduled to be executed, but you can save him (or finish the Sith's job). To free him, turn all the wall switches red: first hit the middle switch, then each end switch and you'll receive Light Side points. Turn them green to get some Dark Side points for killing him.
4. Elevator down to Sith Governor's room. This elevator is guarded by a security droid with heavy shielding. Physical weapons or disruptor/ion guns are your best bet, or, disable the shields using one of the computer consoles (takes a lot of spikes). To open the elevator, either slice a computer terminal or get a passcard from the barracks just north of the elevator.
5. Sith Governor's room. Be very, very prepared before opening the door. He's a dark Jedi and he's very tough. Fortunately, he doesn't have a lightsaber; or, maybe, that's unfortunately, since you probably don't have much in the way of physical damage shielding yet. The Taris launch codes are on his remains. Make sure to loot the footlockers in his room.

The rest of the Sith base is completely optional, though there's plenty of experience and loot to be found. Disabling all the sentry droids through one of the computer panels will make your stay more pleasant.

6. Control room. Basically lots of enemies and a couple of computer consoles.
7. Back hallway. Use this hallway to get to the control room and you'll find a broken down sentry droid. Repair it and send it on its way to give you more firepower against the large number of enemies in the control room.
8. Armory. Lots of good stuff in here. Definitely worth a visit.

Clean Up

You have now almost reached the endgame on Taris. Once you take the launch codes back to Canderous and tell him you're ready to go to Davik Kang's estate, there's no going back. Finish up any loose ends now (bounty hunter quests, dueling champion, rakghoul serum, etc.) and then get ready for the final part of your journey on Taris...

Davik Kang's Estate

1. Once you've been introduced to Davik and taken a tour, you are put in this room with a warning to remain in the guest wing. But when did you start paying attention to warnings?
2. Slave quarters. You can go here to get a massage, but it's not worth the effort.
3. These other rooms all have locked doors and the occupants are peeved at being disturbed.
4. Calo Nord's room. He's not home, but his stuff is. Loot his (locked) footlockers for a nice haul.
5. Davik's "throne room". No, he doesn't have delusions of grandeur. Not at all!
6. Barracks. There's a security terminal in here where you can wreck the usual havok (assuming you have the skill and the spikes).
7. "Guest" room. There's a guy being tortured in here. Free him from his confinement cell and he'll reveal he is the pilot of Davik's ship Ebon Hawk. He'll give you the codes to lower the security shield on the ship, which is the whole reason you're here in the first place.
8. One of Davik's "investors" will release a horde of guards from the room next to him, but it's worth it as he has some nice loot in his footlockers.
9. Spice lab. There's a whole plot about the manufacture of "spice" (a type of drug) that, apparently, got taken out of SW:KotOR near the last minute. There's a whole level of the Black Vulkar base that is inaccessible to the player (unless you know the cheat codes to get there) that is full of spice manufacturing. I guess the concept of drug addiction was too controversial for a T-rated game; but, Davik's spice lab is still around, making you go "Huh?" when you first encounter it.
10. There's another security terminal in this barracks. Once you have the codes to Ebon Hawk's security system, you can use one of these terminals to shut it down. There's also a passcard that you can get from a wandering guard so you don't have to use computer spikes at all.
11. Ah, the hangar. You're free at last! Well, not quite. Davik Kang and Calo Nord show up to ruin the party. Lots of grenades (again) and concentrate on Calo. As soon as he's low on health he'll threaten to blow up the whole hangar. At that point, fate (in the form of a Sith bombardment) intervenes and Calo and Davik get blown up real good. Steal the Hawk and head for Dantooine...Don't forget to loot Davik's corpse on the way out, his war suit is the best armor you've come across to this point!