Golden Gate Park
I personally think every visitor to the city of San Francisco should try to come and visit the Golden Gate Park. It is too bad it is not in the city center just like Central Park is in New York City. It is very beautiful nonetheless and it is the site of many must see attractions like the De Young Museum, the California Academy of Sciences, the Japanese Tea Garden, the Dutch windmills, and the Observatory among others. Unless one has a car, I don't think this place can be explored in its entirety in a day. It's just too big.
I highly recommend a visit to this park. The open space and the greenery that abounds here is simply picturesque.
It can easily be reached by MUNI Bus from Market Street in downtown. I normally take Bus No. 5 and get off at 6th Avenue.