I'd highly recommend the Fauzi Azar Inn for anyone going near Nazareth. I haven't stayed there while hiking, but I spent a few days there on another visit to Israel, and was greatly impressed. It's gorgeous, comfortable, well-priced, and staffed by nice people.

Now that I think about it, I don't know of any other hostels near the trail in the north. I'm sure there are more in Nazareth, but as the Fauzi caters specifically to hikers, it's hard to beat.

I guess there are probably some in Tiberias, but I thought it was nicer to camp near the lake.