Thank you all for the excellent advises. We reevaluated out plans and decided on following: arriving in Tel -Aviv as 2:30 am on Friday (we are coming from Rome vacation, no jet leg) will catch a bus to Eilat -6:30 am- arriving at noon. Spend a day in Eilat by the Red sea snorkeling; Saturday visit Petra ( heat not an issue for us ); Sunday rent a car and driving to Jerusalem with a stop by the Dead Sea. Arriving in Jerusalem on Sunday night, (and as per above mentioned suggestions) instead of running around the country like chickens without heads, will spend full 5 days exploring Jerusalem.
How about this plan?? Any suggestions??
Thank you ALL again.