The large restored caravanserai in the village of Karadayi is worth a visit if you are traveling from Kayseri east to Pinarbasi. It is about 50km from Kayseri on the left-hand side of the road if you are heading East. We visited the Han as part of the excellent Eastern Turkey tour organised by Alkans in Van - so I'm not sure how easy it would be to get there by public transport.
The closed courtyard is currently fitted out as a wedding venue but this does not distract from an appreciation of the 13th century architecture. Don't miss the shaped keystones in the arch of the doorway leading into the closed section - exquisite craftsmanship.