Combining an exciting seismically-carved geographic and a relatively mild ocean-moderated climate San Francisco, and the surrounding areas offer some phenomenal ways to enjoy the outdoors - walking and bicycling are great roof-free ways to get around town :)
Destination-wise, the Golden Gate Bridge and Golden Gate Park are required, but just the beginning. In fact, there are very few locations in SF without some view, hill or other feature of natural interest. Some of the best ones are the (more) industrial waterfront stretching along the Embarcadero from AT&T Park out to Pier 39, and continuing in (somewhat) less-developed form past Fort Mason along Crissy Field out to the Golden Gate Bridge.
West from the bridge, Baker Beach (including China Beach) and the Lands End Trail are stunning and feel like a world away from urbanity. The west coast of SF, from the Sutro Baths down the expansive Ocean Beach are somewhat more developed, but amazing nonetheless. The sometimes-forgotten Fort Funston in the southwest corner of SF is a mecca for hang-gliders and dogs... and possibly hang-gliding dogs, but I haven't seen one myself :)
The interior also has some special spots - Twin Peaks is on the tourist circuit for good reason (Kite Hill is not, and within walking distance of the Castro). Corona Heights and Buena Vista Park are beautifully situated on the Castro side of the Haight-Ashbury. Dolores Park is the busiest park in the city, and offers a stunning view of Downtown - along with the many nearby Mission delights. On the south side, Bernal Hill is gorgeous and often warmer than the rest of the city.
Beyond SF, getting on the bay is a great way to go. Blue & Gold Ferries offer bay tours in addition to regular service to Sausalito, Tiburon and Angel Island among others... or Sea Trek Kayaking can scratch that personal-water-craft itch! And, of course, Alcatraz is naturally stunning in addition to its penal charm.
There are many unbelievable spots going north - the Marin Headlands (just across the bridge), Rodeo Beach, Tennessee Valley, Mt Tamalpais, Muir Woods, Stinson Beach and Point Reyes to name a few - and beyond these, Napa and Sonoma.
