Hi Sarah,
If you have time and want to go hiking, go to Mitzpe Ramon. It's the desert and you have amazing landscapes there, with a crater. You can go by bus, you don't need to book a tour for anything in this country. There is a hostel there, they can give you lots of advice "The green backpackers"
Hi Sarah... recommend seeing Masada ... the siege and story of the long Roman campaign to sieze this Jewish settlement/fort by the Romans and the outcomes is fascinating history as well as the proximity to the Dead Sea I still remember as highlights of a similar trip to Israel .. floating on the Dead Sea “water” you also wont forget.