Outside the Wall, Jerusalem
There are many little surprising corners and buildings in Jerusalem. I found the windmill very funny, and suddenly I felt very Dutch again ;-)
Don't forget to visit mount of olives. It has a beautiful church and nice nature surrounding it. You can also go mountainclimbing here.
Visit the local markets. Buy yourself fruit and clothes. The market just outside Damascus Gate is extremely nice.
Go and see the people just outside the wall. Visit the local market. Here is where I saw this tea and coffee salesman. He also sold cold drinks.