Wall
I highly advise that a climb around the walls is a must. Walking even half the wall will give a better view of the city, see homes that have new and old tiles, and to get some fantastic pictures of the view.
You can choose to walk all of the wall, or only part of it. Walk along the ocean side, or along the hillside, no matter which you choose, the views are spectacular, and one to share with those at home.
Along your journey, you will come across watchtowers, little shops of locally made treasures, and even a chance to grab some food.
The climb up and down is steep, so be prepared, and since the walls create a saddle form around the city, know that the walk around contains additional stairs.