We enjoyed our walk, with a stop in the Ambrosia Cafe for iced coffee and an absolutely delicious chocolate brownie (that was really a warm chocolate fudge cake), and luckily, with the map were able to find our way out. Definitely a delightful experience.
So, a little more experienced and educated, we now decided to make our way a little further into the city, heading for the Bozdogan Aquaduct. It should have been easy to get to, we had a good map, knew where we were, and knew where we were going to.
Looks like we are going to have to find a way to come back then.