Thanks for all the suggestions.
We went to Gulsehir and Ortahisar today (among other places)- definitely worth visiting. Gulsehir's Open Air Palace ruins are nice and quiet, and the church is beautiful and photography is allowed. Ortahisar's castle is a good viewpoint. Also wanted to visit the church there but it seems to be closed.
We will visit Ihlara in the coming two days. Our balloon ride was cancelled today- hopefully the weather is fine tomorrow!
