Check out the various vantage points around "Captain Burke Park" for that iconic elevated view of the bridge with the riverside skyline in the background.
My daughter used to start telling a story every day when we got onto this bridge before or after school. She always stopped at the end of the bridge. Planners make spaces, people story places.
If you are crossing the bridge on foot and find the vibrating / shaking of the bridge unnerving ... The tip is to keep walking and not stop. You'll feel the shaking more when you are standing still.
There's a cool walkway right under the northern end on the way from the city to Wilson's Outlook. It's a good walk and lots of great views along the way.