There's nothing ultra special about this bridge, besides it being an iconic attraction synonymous with the bay area, and even California as a whole. For this reason alone, it's worth making it across this bridge at least once. And my suggestion is to do it by biking.
Driving, won't let you pull over to take pictures or anything; it might as well be any other bridge when you're driving and have to focus on all the vehicles around you. Walking is fine, but can take longer and monotonous by the time you have to walk to and fro. Biking is ideal because you can go fast enough to feel the coolness emanating from the bay. Yet you can stop at any point to take pictures, or take in the view. With my bike, I was able to ride down to the wharf, which offers another unique view of the bridge, and a few people fishing for a catch.
The only downside to biking is that the side of the bridge dedicated to riders doesn't offer as much of a view of the city. The other side for pedestrians offers the view of the historic Alcatraz prison (another must-visit in San Francisco.) But you can park your bike at Sausalito and cross over to the other side through the pedestrian underpass beneath the bridge.