Places I'd reccomend to visit in Galilee are the Dishon river, Amud river, Dugit beach (although that's more of a Golan than Galilee...), a nifty hole named Kadita which is near Sefad, Zichron Ya`akov and the Baron's parks nearby.
If your'e in shape you can go on and climb on Mt. Tabor and the Carmel ridge (I suggest crossing it east-to-west from around Kibbutz Yagour). Hitch hiking through the kibbutzim along the Lebanese border wasn't a bad idea for me as well.
Places to avoid at all costs are Tiberias and downtown Haifa. They stink.