Recently while visiting San Francisco I put it on my vacation itinerary to check out Muir Woods. As a bona-fide city girl with a phobia of lizards I was a little unsure about being in the out-of-doors, but my desire to see the Redwood trees told me to suck it up buttercup and make the trip! I am so grateful that I did!
Located just 11 miles north of the Golden Gate Bridge makes Muir Woods perfect for someone wishing to see nature and still have all the comforts of a major city nearby. Honestly though after the first five minutes there even this city girl was contemplating hiking more often.
In 1908 this grouping of redwoods, some between 400-800 years old, was established as the Muir Woods National Monument. It is open to the public every day of the year and is free for children 15 and under. As I am writing this the current price for 16 and over is $10, but please check their site for possible price changes. 
