Thanks for the info. What I am trying to do is find a tour with pick up in Tel Aviv and drop off in Jerusalem but with the day I need there are only a couple options. Flight leaves Ben Gurion airport at 5:20 AM so public transport options are out and will need a taxi for at least that leg. Hotels chosen so far are the Sheraton in Tel Aviv and Eldan in Jerusalem which does not charge for parking.
Are there interesting sites to see on the drive from Tel Aviv to Jerusalem?
Does Israel have Uber?