After the last chapter, you might not like the Lannisters, but give them a chance: you haven't spent a lot of time with Tyrion yet. This chapter takes place four days after Bran's fall; Bran is in a coma and will be crippled for life, but he's alive.
Tyrion likes reading (so we like him) and he hits Joffrey when Joffrey refuses to pay his respects to the Starks.
When Tyrion tells Cersei and Jaime that Bran will live, Tyrion can tell that they know something that they're not telling him. We also see the general family dynamic between these two: Cersei hates Tyrion but Jaime loves him.
Also, Tyrion plans to travel north to see the Wall.