I've done a few calculations on my own.
Basic transport: Airport to Akko, Akko to Tel-Aviv (by train), T-A to Jerusalem (bus), J'm to airport(sherut) is about 190 NIS. But you have to add more if you take buses from Akko to Zfat, J'm to the Dead Sea, etc. So the total will be at least 300 NIS, or 30 NIS/day. Add two bus rides every day in the cities and the total is 45 NIS/day.
Dorm rooms in the better hostels in Tel-Aviv (Hayarkon48, Gordon Inn) are about 100 NIS/night. Cheaper one (Florentine are about 75). I assume you can find cheaper in the Old City in Jerusalem and Akko. So the average will be at least 75 NIS/night.
Entrance fees: Most museums and sites charge 30-50 NIS entrance (some are free). Assume minimum 50 NIS/day.
So we are already up to 170 NIS/day. This leaves you 60 NIS for food and miscellaneous. Your hostel might include breakfast (the better ones probably do), so you have no more than 50 NIS for lunch and dinner. That isn't enough even for street food - hummus, falaffel, pizza slices, etc.