The dead sea is an attraction In israel and in the world , becuase of the salty water that makes you float on your back and also because it is the lowest place on earth.
This is not too close to Eilat (2-3 hours drive) but you will enjoy beautiful landscapes and relaxing place.
You can check my Dead Sea (En Gedi) page for more details
An ideal day out is to a spa near the Dead Sea. A wonderful place for relaxation in a sulphur bath followed by a Dead Sea mud bath and afterwards a swim in the Dead Sea. Don't miss it.