İzmir was until 1930 known as Smyrna (Σμύρνη or Σμύρνα in Greek). That was the original name of the city settled by ancient Greeks later conquered by Alexander the Great, and followed by the Romans. It was also one of the seven churches in the Book of Revelation.
There were really two ancient Smyrnas – the old Smyrna and the new Smyrna. Old Smyrna was settled in the 11th century BC and is located at Tepekule. This guy named Alexander came along in the 4th century BC and conquered old Smyrna. Anyway, he was hunting up at the top of a nearby hill named Pagos (Πάγος) by the ancient Greeks and decided to take a nap under a plane tree. As he slept, he had a dream in which he was to found a great city built on the hill. His dream was eventually carried out but only after his death. The settlement of old Smyrna was abandoned and the people relocated to the new site of the city.
On very same hill where Alexander the Great had his dream sits a Byzantine castle that was rebuilt by the Ottomans. The castle was named Kadifekale (Velvet Castle) by the Ottomans. It’s also an important site for Christians. During Roman times, St. Polycarp, the bishop of Smyrna, was martyred at the site of the castle in 155 AD. Admission to the castle is free.
Inside the castle are the remains of a Byzantine cistern and a small Ottoman mosque. Everything is kind of run down and unimpressive, but the views are stunning.
You can reach the castle by walking up through the maze of streets near the ancient agora. However, the streets up to the castle, and the castle itself, are located in a slum and one of the few unsafe areas of İzmir. I would not do the walk up to the castle alone as I did. If you really feel a need to visit, for safety purposes, a taxi is the best bet to get up there. Again, the castle is not a must-see unless you are really interested (oh, but the views!).
If you do choose to walk up, the most interesting thing I saw was a road that was completely collapsed. There’s nothing special about the neighborhood on the way up.