During your time in the Holy Land, please stay with your Guide (and your Group) throughout the full duration of your tour.
Your guide will advise you when you have “Free Time” on your own. Always inquire with your Guide first, about any sites you would like to revisit, or where is the best place to shop when looking for a particular item. They will advise you of the best way to get to both.
When traveling on you own, you need to maintain a greater level of awareness of your surroundings. When walking, be aware of anyone following you. A good rule of thumb if you suspect someone is, cross the street to see if they cross also. You should stay away from areas with additional security and avoid large gatherings and demonstrations. Once when I was traveling in Brussels, I came out of the hotel and in the middle of a demonstration with people yelling and marching. When I found out it was teachers marching, I felt pretty safe.
For additional safety, see US Department of State recommendation for U.S. citizens.