San Francisco has nothing to compar to the Appalachia and the Ozarks. The only forestry near the bay area would be the 559 acre Muir Woods National Park. It is actually in Mill Valley, Ca, Muir Woods is open every day of the year, including all holidays. Park hours vary throughout the year, but the park is generally open 8:00 a.m. to sunset. You will see the tallest type of tree in the world, the Coast redwood, sequoia sempervirens, as well as the countless other plants and animals that are part of an old-growth redwood forest, including tanoak trees, ferns, redwood sorrel, stellar jays, black-tailed deer, and banana slugs, to name a few.
There is also the Calaveres Dam, located at the Alameda-Santa Clara County line. The dam is a 230 foot high barrier which holds the largest drinking water reservoir in the 9 county region. Since its location is on an active fault zone, dam regulators drained the reservoir to about a third of its capacity. The Calaveras reservoir sits in the Alameda Creek watershed, which drains most of the southern sections of the East Bay, including the southern slopes of Mount Diablo