Whenever you feel like it
Hopefully you're cruising the Pacific Coast Highway when you check out the bridge so stay oceanside
For just being a bridge there's an awful lot to do here. Sadly I'm going to focus on what you shouldn't do, which is jump off the bridge. If you're thinking about it and you make it far enough to get yourself all the way out there on the bridge you're going to see a bunch of these:
I don't know how long I sat there staring at these things wondering what in the world they were for. I began to imagine what I would do if I saw an one hundred foot tsunami coming toward me. Would I pick up the phone to talk to some sort of counselor? What are they going to say "you're going to get washed off of that bridge and into the bay, but there's still hope. You can swim, right?" Or how about an earthquake? Then I read a bit more carefully and saw that it was for people who just couldn't take it anymore and had to jump. It's extremely sad that enough people take such drastic measures that they require crisis cousneling phones on the bridge. Oh what oneupsmen will do when they can't oneup their neighbors.
The park is great though. If you aren't heading here to make the plunge, have a look around, cross the bridge, go up into the hills, do anything, just DON'T JUMP - you could just move to a less crazy lifestyle in the countryside. I'm hoping to be back someday to do the break out of Alcatraz triathlon. Not sure, when I'll be up for it, but it will happen eventually.