There's more to the Golden Gate Recreation Area than the Golden Gate Bridge. A great place to explore is the Marin Headlands just north of the bridge. Drive west on Bunker Road a couple of miles to the Marin Headlands Visitor Center for trail and wildlife information. You're likely to see a few mule deer along the way. Cyclists share the road so be mindful of their presence.
The coastal trail has a spectacular view overlooking Rodeo Beach and the lagoon. About a mile south from this view is Point Bonita Lighthouse. The lighthouse is only open a few short hours three days of the week, so check at the Visitor Center for the tour schedule before walking a half-mile down the trail.
Golden Gate National Recreation Area includes the largest collection of military fortifications in the U.S. Explore these abandoned bunkers, but stay on the trail as there are many endangered plant species in the park.
The photo of a bobcat on this webpage was a lucky sighting. Most bobcats will avoid people and are active mostly at night. I didn't have enough time to put the telephoto lens on, but with my higher resolution camera I was able to capture enough detail before the cat hissed at me and hid in the brush.