After a visit to the agora I climbed towards Kadifekale (Velvet Castle). From there one gets great views over the city (and a nice fortification in the bargain).
Inside the walls is a subterranean structure that reminds me of a (Roman) cistern, which would be fitting for a castle. I am not certain if that's what it is, though. As for that, I wsas informed there was an underground tunnel from the Citadel to the Agora.