Input on itinerary for Israel & Jordan

Hello all!

I am travelling to Israel & Jordan soon, and have very loosely planned out my trip. Just wanted to get your input - it's not a long trip, so just want to get my priorities right...

June 28 (Sat) Arrival in TLV early morning - probably head to Jerusalem directly
June 29 (Sun) Jerusalem
June 30 (Mon) Jerusalem
July 1 (Tue) Jerusalem (Bethlehem half day?)
July 2 (Wed) Jerusalem (Ramallah half day?)
July 3 (Thur) Jerusalem
July 4 (Fri) Jerusalem (Dead Sea - a friend may drive me out there)
July 5 (Sat) Fly to Eilat and continue to Petra, hopefully in time to see sunset there
July 6 (Sun) Spend all day in Petra, take evening bus back to Amman.
July 7 (Mon) Spend all day in Amman (probably just stroll around the city - I'd imagine plenty to see? but if not, maybe Jerash?)
July 8 (Tue) Departure from Amman

It's quite loosely planned, as you can see...I have the blessing of being able to stay with a friend in Jerusalem and another in Amman, so I can pretty much change along the way, except for the flight to Eilat that I should probably get soon. The "loosest" part now is the Jerusalem days - understanding that I could easily spend weeks in that city (love history, culture, markets, architecture), I am thinking of going straight to Jerusalem when I land to maximize time there. I may head out to TLV for a day or a night to see the beach (I really, really want to be on the beach for a little bit).

Any input appreciated!