Just 12.4 miles (20 km) north from San Francisco is the Muir Woods National Monument. Though the park isn’t as big as the others, it’s one of the most accessible parks on the list, so it should come as no surprise that it get the most visitors. In spite of its size, the park is home to many beautiful trails with different lengths and terrain. website
Tip: Try to arrive early so you can find a good parking spot, as it does get crowded in the middle of the day.
If you are interested in family adventure, this video about redwoods is a must-see.