As this is a private tour you can tailor make the itinerary for Jerusalem and the northern part of the Dead Sea to your liking. Here is a suggestion of how you could spend your day. Start by taking in the panoramic view across Jerusalem from the Mount of Olives. Many Biblical events took place on this mount including Jesus' arrest in the Garden of Gethsemane. The Mount of Olives is the site of an ancient Jewish burial ground with about 70,000 tombs dating back 3,000 years.
Drive down the mount and through the Kidron Valley to enter the Old City on foot. Walk through the Armenian Quarter where you can see their exquisite Armenian brightly colored painted ceramic tiles. In the Jewish Quarter see the excavated Byzantine Cardo which was once the main thoroughfare of Jerusalem. Continue to the Western Wall, the most sacred site in Judaism. The wall is the only remaining part of the ancient Jewish Temple which was destroyed in 70AD. In the Christian Quarter you could follow the Via Dolorosa retracing Jesus' route to his crucifixion and then visit the beautiful Church of the Holy Sepulchre. Before leaving Jerusalem spend some time exploring the Old City market.
Drive south through the Judean Desert and pause for a photo op at the sign indicating that you are now passing below Sea Level. From the road you will be able to see the ancient city of Jericho in the distance and the mountains on the Jordanian side of the Jordan River. When you reach the Dead Sea you can enjoy the beach and float in the saline-rich water. The Dead Sea region is known to have therapeutic benefits due to the high oxygen level of the air, diminished UV sun rays, the mineral rich Dead Sea water, Dead Sea mud which can be used as a face and body mask and the sulphur pools. After a relaxing time on the shore of the Dead Sea you will be returned to your hotel rejuvenated.