This forest was in part planted by the KKL (pine trees, a few cedars as well) and in part is a natural oak forest. It occupies the mountain slopes going down towards the Nahal Tziv'on wadi, and the nearer you get to the bottom of the wadi the richer and more varied the vegetation becomes.
There is a picnic site near the road in a part of the forest named after the late Prime Minister Yitzhak Rabin and his wife Leah. From there, a 4km circular hiking trail (medium difficulty) will take you through the forest down to the Tziv'on wadi and back up again. It's a beautiful hike any time of year; there is flowing water in the wadi only during part of winter.
A narrow winding road goes to the summit of Mt. Shifra (Har Shifra), 743 m above sea level.
There is a lookout tower (built by the KKL to spot forest fires) which is open to the public at all times.
From the viewing balcony there are sweeping views of the Meiron mountains in the south-west, the Dishon canyon, hills of Gush-Halav, Dalton heights, and when visibility is good the northern Golan.
There is a picnic site nearby.
Bar'am National Park is the home of the 4th century AD synagogue and the ruins of the Arab village of Bir'am. The park is also part of an ancient oak forest and offer great views of the upper Galillee mountains.
Here are some useful information about the park. You can find more in the link below.
Adults NIS 18, children NIS 6
This picture was taken from within the ruins of the Ikrit church. Until 1948 there were two Arabic villages in the area, Ikrit and Bir'am. During the war the villagers were evacuated. They were promised it was temporary and when the fights were over they could go back. After the war, they wanted to go back to their lands, but then they were refused. The lands were given away to the nearby Kibbutz Bar'am. During the years, the Israeli supreme court decreed several times the government should allow them to go back, but this was never done. The ruins can be seen in the national park.
Recently, the villagers were allowed to rebuild a church at the spot as can be seen in the pictures. You can read more about it in http://www.mliles.com/melkite/indexmelkiteotherholylandikrit.shtml and http://www.kibush.co.il/show_file.asp?num=1311.