I was in Palestine in 2000, so take this with a grain of salt - I am not sure how easy and safe it is to travel around the West Bank nowadays. I heard the wall makes things difficult.
The cities in the West Bank that I liked best were Bethlehem, Hebron and Jericho. All should easily be reached from Jerusalem. When I was there all it took was a shared taxi from Damascus gate in Jerusalem. Those are also the cities in the West Bank that get the most tourists and have the most attractions. Security in Hebron will be the most tight, the city is practically a powder keg. Jericho should be safe if you can get there.
It should also be possible to travel from Jerusalem into Jordan via King Hussein bridge, but to do this you need a valid Jordanian visa. You cannot get a Jordanian visa at King Hussein bridge.
There are two ways to get a Jordanian visa.
The usual one is to fly into Amman at the very beginning of your trip, get your visa, cross into Israel at King Hussein bridge (thus not getting stamped out of Jordan), touring Israel for about 2 weeks and then return to Jordan via King Hussein bridge. This way is done to hide evidency of a stay in Israel, which is possible if you can convince the Israeli boarder guards not to stamp your passport when entering Israel.
The second option is to apply for a Jordanian visa in Tel Aviv.
When faced with applying for the visa in Tel Aviv I decided to take the bus down to Eilat, see some sights along the way (Masada, Dead Sea, Mitspe Ramon, Bersheba), cross the border at Eilat/Aqaba and then go to Petra. I had wanted to go down to the Red Sea anyway, so it was just easier to get the Jordanian visa at the Eilat/Aqaba border crossing.
[ Edit: Edited on 20-Aug-2009, at 12:38 by t_maia ]