Joffrey, Sansa, and an array of goons stroll through King's Landing. Here's Joffrey's idea of small talk: "As soon as you've had your blood, I'll put a son in you." Aside from what that tells you about our budding young sociopath, it's worth noting that Sansa is still quite young. So I guess she should be cut a little slack. A little. Joffrey leads Sansa onto a high bridge to show off his new addition to the Red Keep: heads on pikes! Specifically, Eddard Stark's head on a pike. Sansa cannot maintain her feigned indifference and cries out that he promised he'd be merciful to Ned. Joffrey's idea of mercy is "a quick execution" as opposed to boiling oil or whatever other torture implements they had lying around. That throne looks like it could probably be used for something nasty. Sansa hasn't looked at her father's head, but Joffrey orders her to. So she stares blankly at it for a bit before asking how long she has to do it. The answer is, "As long as it pleases me," which is a little vague. I think she's implicitly accepting that he's up to how long she has to watch.
He changes the subject to the head of Septa Mordane. So she did, in fact, die. Good to know! Sansa still won't react, so Joffrey ups the ante and says that he'll bring her Robb's head. She looks him in the eye and answers, "Or maybe he'll give me yours." Joffrey is instantly furious at being defied, so I don't know what he was hoping for. He tells her that his mother has told him that a king should never hit his lady, which is an understandable position for Cersei to hold, when you think about it. Because of that time that Robert hit her. That is the incident to which I refer. Anyway, because Joffrey is a nasty piece of work, he has one of his goons smack Sansa across the face. It draws blood. She looks down at the long drop off the bridge and then walks toward Joffrey with that evil look that Stanley Kubrick was so fond of. But before she can reach him and push him off the bridge to a richly deserved death by plummeting, the Hound stops her under the guise of giving her a hanky to wipe the blood off her face. Joffrey leaves and the Hound recommends that Sansa do what Joffrey wants. He also thinks she should keep the hanky, because she's going to be getting smacked in the face by an endless succession of goons from now on. Sansa looks at Ned's head again.