I got to Israel during Passover this year without any kind of reservation. I stayed within the old city for a week and found a place to sleep very easy (Petra Hostel at Jaffa Gate, but there were others of that kind available). During my stay I went by bus to the Dead Sea, Eilat and Tel Aviv and got the tickets on the same day at normal prices (http://www.egged.co.il/Eng/).
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