What areas offer serious soul farming?
There's two more places I can think of. In order of progression:
Painted World of Ariamis
This is the place where I did my farming after Dark Root Garden wasn't cutting it anymore. First, you will need to:
Find the Peculiar Doll in the Undead Asylum on your second visit. For instructions on how to return to Undead Asylum, check this video. The doll can be found in the same cell where you started the game.
Reach Anor Londo and locate the big room where the Painted Guards are. You will find a huge painting on the wall. Descend to the floor level and touch the painting to be transported into the Painted World of Ariamis.
Progress through the level until you reach a sort of town square, where you will find a slew of Phalanx mobs. These are the creatures you will be farming.
Across this courtyard, you will find a door that opens up and leads you to the starting bonfire.
You will need an AOE damage spell for this method. Poison Mist is a good choice for low levels, since Phalanx are weak to poison. They move slowly, so you can run up to them and cast Poison Mist one or two times while moving in circles around them. Just wait for a few seconds and they will die. With the Covetous Silver Serpent Ring equipped, this method will net you around 9000 souls in a few seconds. Just run back to the bonfire and repeat.
If you are a caster class, you will be able to speed up the farming by using strong AOE spells. For instance, I play a faith build character. My Wrath of the Gods spell managed to kill all Phalanx with a single cast, netting me 9000 souls every 20 - 30 seconds. I spent more time running up to the town square than killing them. The Homeward miracle will speed up this process considerably.
Now this method requires you to side track from the main story progress. Another method you can try, which doesn't require you to do any side-quest is farming Dark Anor Londo.
Dark Anor Londo:
After beating the Ornstein and Smough encounter, you will meet Gwyneavere. If you hurt her she will disappear and Anor Londo will become Dark. Warning: Making Gwyneavere disappear means you won't be able to join the Princess' Guard covenant for the rest of your current play-through.
In Dark Anor Londo, only Painted Guards and Silver Knights will remain, the rest will be gone, including the giants and archer right outside Ornstein and Smough's fog wall. Instead, you will find two NPCs here. You can kill them for around 6000 souls with the Covetous Silver Serpent ring equipped. The trick is, they will only respawn if you leave Anor Londo and return. However, you can use Homeward Miracle to return to the previous bonfire where you rested at. The NPCs will also reappear.