If you end up in Jerusalem, there are alot of options, (many of which i have not yet explored), but more than once i have stayed at the Petra Hostel, and I can whole-heartedly recommend it to anyone.
The Petra Hostel is Just inside the Jaffa Gate, and looms over the entrance to the Arab Markets. It has the best view overlooking the Old City (second only to that from atop the Citadel of David).
If you are trying to go cheap, then you can't beat the Petra's prices. I have never even bothered staying in one of their rooms, because for 20nis ($5), you can just go sleep up on the roof, where there are like 30 old mattresses just laying around up there. They don't give you sheets. There is no breakfast. There is really no anything, but if you are going for a place with personality, rather than comfort, this place is it.
In operation since 1830, the Petra was then known as the Hotel Mediterranean. It was the first real Hotel in Jerusalem. Mark Twain and his group stayed at the Petra when they visited Jerusalem in 1867, and Herman Melville is said to have written part of Moby Dick in one of the Rooms.
Now, this 4 story building, which is always bustling with guests, is old and run down, but in a really cool sort of way. It’s not dirty or bug infested or anything like that, but there is crappy furniture all over the place, the stone tiles on the floor (original) are all cracked and sometimes move under your feet. Some windows are broken, and nobody really cares to fix them. One time, when I was washing up in one of the little bathrooms, the faucet fell right off the wall and landed in the sink. There isn't a right angle in the place, and there are also usually some cats just living in there. The place is amazing.
But the reason that i would recommend the Petra is because of the people there. First of all, the Guy who runs the place is this really cool guy named Gabriel, and he is reason enough to visit the Petra. He looks like he's straight from Africa (he's not), wears these one-piece cloakish garments that he makes himself, has started his own religion (variation of Judaism that has a unique interpretation of Torah and who the Messiah will be), and who loves to talk about prophecy and the Biblical calendar (but watch out, if you're a follower of Jesus/Yeshua, he will try and convince you not to be!). He lives on the roof with his wife and kids. Everyone should talk to him.
You'll also meet lots of interesting guests at the Petra, because it seems to be kind of a magnet for some of the odd folk who find their way to Jerusalem.
Anyway, there are lots of other hostels in the Old City, such as the New Swedish Hostel, and the Black Horse, but every time I go to the Petra, i leave with stories.