It struck me that with all these discussions of what to wear, no-one mentioned this:
If you are going to the Old City of Jerusalem, the City of David or similar sites, wear shoes with a really good grip on the soles. In many places the flooring is of Jerusalem stone smoothed by many generations of pilgrims' feet, and while it's very beautiful, it can also be (a) uneven and (b) extremely slippery, especially if there is a slope or if it is wet, and (c) very hard on your feet/knees.
Good rubber-soled hiking-style sandals or sneakers are fine. However, you do need more grip than for regular walking - I practically skied down the path down from the Old City to the Sultan's pool the other day in my well-worn Naot sandals, despite the reasonable amount of remaining tread on the soles of these sandals, which I wear with no problems the rest of the time.
Just an advance warning!