Tyrion is sent off with Haldon Halfmeister and Ser Rolly Duckfield to go and meet Griff by the Rhoyne, so that they can then travel to meet Dany. We learn that he's well versed in his history, especially Targaryens and dragons. We get a bit more reminiscing about how awful a father Tywin was: he told Tyrion he couldn't go on holiday because he'd married a prostitute, even though we now know she was not, in fact, a prostitute, and Tywin knew this all along. If Tywin was so smart, how come he couldn't overcome his disgust at Tyrion and see how useful he could be. He even got the drains working properly at Casterly Rock. Never underestimate the importance of well-functioning drains!
Illyrio has sent along chests of useful items, including clothes, gifts for Dany, and a letter to Griff which, suspiciously, Griff burns before Tyrion can read for himself the parts about handing Dany Tyrion's head on a platter or whatever underhand scheme is undoubtedly brewing beneath the surface. Griff isn't all that friendly, but Tyrion's knowledge of which lords are which and how to look after dragons might actually be useful to Dany, so there is some hope this will go well.