Finally, Eddard arrives at King's Landing. (The trip has been no fun, with Sansa and Arya blaming each other for what happened to Lady and Mycah.)
But he can't rest because there's work to be done: Eddard has to attend a meeting of the small council (the advisors to the king, called "small" because it's a very select group). The small council is Robert (who never attends); his brothers Stannis (who left for his home castle, Dragonstone) and Renly; Barristan Selmy (who isn't there right now); Petyr Baelish, master of coin; Varys, spymaster; and Grand Maestar Pycelle, who is the master of being old.
Eddard is upset because (a) Robert wants to hold a tournament to celebrate the new Hand of the King; and (b) the throne owes a lot of money to people, including Tywin Lannister.
After the meeting, Petyr takes Eddard to meet Catelyn, where they discuss the weather and their favorite sports teams. Oh wait, no: they discuss the assassination attempts on their son.
Petyr advises caution: they can't just go accuse the queen of murder. So Eddard tells Catelyn to go home and tell people to prepare their defenses. Just in case, you know, war happens.