How much (more or less) is laundry service at budget hotels/hostels in Israel? Are there any public self-service launderettes/laundromats?
I don't know what laundry costs in hotels/hostels. There are a few launderettes in Jerusalem but they are not very common. There is one on Jaffa Road, very near Haturim light rail station (between the central bus station and the Mahaneh Yehuda market). It's hidden inside a little shop selling snacks, bags of crisps etc. It's called Rotem Laundry, but there is no sign in English. It's open till 11 p.m. (except Fridays, when it closes at around 5). Closed Saturdays during the day, but it opens after the end of Shabbat (so around 8:30 p.m. this time of year).
From the light rail stop, walk about 100 metres in the direction of the Old City. There is a small group of five or six tiny shops on the left, and that's where you'll find the launderette.
http://tinyurl.com/kef9ohv
I think it's the place with the green table and chairs, or else the one next to it!

If you are in Tel-Aviv try "Hamachbesa"
This company has a number of launderette branches around Tel Aviv, here are two.
• 102 Ben Yehuda St.
• 6 Kikar Dizengoff (On Dizengoff Square)
http://or-wash.zapages.co.il/

Some hostels had washing machines and dryers. Take a bit of elastic you can tie up in the bathroom or on the end of your bunk bed and handwash your undies and sox....everyday....save the big stuff for when there is a machine. In the dry Israeli climate your hand washing will be dry by the next morning.