The Dead Sea is a pretty special place, and super super hot in the summer.
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A cool place is dowm from Metsokei Dragot. From Jerusalem go south following the coast. Just before Metsokei's check-point go off the road, walking, down to the sea and continue walking south for 10-15min. There is a small pool there with water and a small river. It is a very chilled place where people walk and bath naked, and one of the only places in Israel where long term wild camping is still possible. After floating a while you can rince in the pool. But you cannot drink the water of the rive so take a lot of water with you! You can get some in Metsokei Dragot, but it's quite a walk. On Sabbath more people come for the weekend.
The north part of the Dead Sea coast on the Jordanian side is very ugly. 15min walk North from the "Samarah Mall" there is a pipe next to the big parking space with water coming out to rince yourself after swimming/floating in the sea. But it is not such a nice place.