2014 Papal tour

I understand his Holiness, unlike previous Popes on their Ho;ly Land tours, arrived in Amman, but he departed from Ben Gurion, right? He did not shuffle across the frontier and depart the same way he came?

Correct. But he doesn't need to worry about stamps in his passport...

From the videos I have seen of his arrival in Israel, I deduce he was transported to Israel in a Jordanian military helicopter.

what hotel did he stay at?

I don't know.

itinerary: http://popefrancisholyland2014.lpj.org/program/

no idea where he stayed

the itinerary you have so helpfully supplied, provides a clue :

Dinner with the Patriarchs and Bishops and the Papal suite at the Latin Patriarchate in Jerusalem.

what, and where is that?

and Papal suite? I've heard of the Presidential suite, but 'Papal' suite? In Italy and perhaps even France and Spain or Brazil, maybe. But Jerusalem? Where there are hardly any Catholics? Are they planning on having a Pope go to Jerusalem every few months in future?

The Latian Patraiarchate building is in the northeast corner of the Chritian Quarter of Jerusalem Old Town. They have a very nice view, but it's not open for simple tourists or pilgrims.

http://youtu.be/DisHrtQRv8k?t=3m9s

To put it this way Jerusalem(with very few Catholics) is a bit more important for us Catholics than say Mexico City(with millions of Catholics). ;-)

I guess they might use the Papal Suite to house other importants guests as well in absence of the Pope. Or perhaps not, but it doesn't really matter in a 2000 year old institution if a suite gets used only every 50 years. :-)