The Skinking City is the second part Taris and were you most likely will be spending level 17-18 if you are on the Republic side. Most of the quest take you in to the collapsed hospital district and specifically in to the ruins of the Dynamet General Hospital. There is a unique quest in this area (compared to other quest in game so far).
You are asked to fight the Rakghouls and get infected with there disease . I found this quest frustrating, it ended up taking me 10 minutes of killing Rakghouls to get infected, the biggest problem was finding Rakghouls (it appears only the larger one can infect you). I was lucky that there were only 7 other people in the planet with me, compared to (100+ i saw on the newbiew words, or 300+ i saw on Coruscant).
Also in this zone is the remains of the Endar Spire. For you lore nerds, the Endar Spire is the ship you start off in Knights of the Old Republic. If you remember in KotOR this ship is being added by Malak’s Sith. Also the planet Taris is the first would you vist in Knight of the Old Republic (300 years before this MMO). What you are viewing today is the remains of the world after the sith had destroyed most of it.