Poor misunderstood monster. He's just trying to give the Golden Gate Bride a hug!
San Francisco has a long tradition of being attacked and/or destroyed in movies, and the first film to show the Golden Gate Bridge as the target of a monster is 1955's It Came From Beneath the Sea, which you can watch this morning at 9:30am on the Movies! channel.
And if seeing the Golden Gate Bridge come to an untimely end is something you enjoy, you'll love this supercut featuring just that.