There's a stone path off the hill on the far side of the church. There are cliffs here too and some really substantial tower remnants. It's really clear to me that the whole hillside was actually pretty well fortified at some point and that maybe fortifications were picked apart during the Ottoman era for building material.
From the path you can also make out the Byzantine metropolitan cathedral. It's dedicated to the Saints Theodore (plural).
My socks are covered in prickly plant bits and so are my boots and pants and I've picked up a few more scrapes on my legs, but I managed to go see some more of the fortifications of the acropolis up close.
There's really a lot more up there to be found than I think most people know about or explore. I'm going to have to search online and see if I can find a formal archaeological site plan of the hill to get a better idea of the outline of walls, towers, gates and other major structures.
Stopped at the Byzantine church of the Saints Theodore...
...and a few other places on the way home. Too many steps. Too much heat. Hard to stop myself with something interesting to see and read about every few blocks. Think I'll try and do the mosques and the museum tomorrow and see if Saints Theodore might be open. Grounds were locked up when I visited. Looks like they have a bunch of Roman era stonework sitting scattered around the grounds.
For now, we rest and do laundry and hydrate and pull clingers of clothing.
Found some information about the church. The two Theodores in question are Saints Theodore Tyro and Theodore Stratelates. The church was first built as a cathedral in 1124, then destroyed in the Fourth Crusade. The present structure was built in 1221 and was hit hard during the Vulcan wars of the early 20th century and required rebuilding yet again, with a long period of rebuilding from 1938 to 1959.