The "Big C" is a giant concrete "C" built into the Berkeley Hills, that overlooks the memorial stadium. Many Cal students go up there to tailgate during Cal football games, and to protect its integrity after the one time Stanford tried to paint it red before the big game.
The Big C also offers spectacular views of campus, the bay, the Bay Bridge, the Golden Gate Bridge, and San Francisco. There is a swing that's there from time to time, which makes for a great picture spot.
The hike up to the Big C from campus is pretty mild and scenic. Not too strenuous, and best paired with a visit to Lawrence Hall of Science, and dinner and dessert at one of the many places in Downtown Berkeley.