Photo by myself on the Brooklyn Bridge, looking toward Manhattan.
There are lanes for pedestrians and bikes on the Brooklyn Bridge. The cyclists ride very fast, so it's best not to stray from your lane. I was almost bowled over a couple times.
The pedestrian walkway is elevated above the level that carries cars. You can see the traffic whizzing by through the gaps in the floorboards. Looking up, you can see a panoramic view through the diagonal cables, from the Statue of Liberty and lower Manhattan in the South to the Manhattan Bridge and Lower East Side, to the North.
Many people were snapping photos Wednesday evening, posing or just enjoying the view. Once across the bridge into Brooklyn, you're in Brooklyn Heights. You can also visit Dumbo, an area named for being 'Down Under the Manhattan Bridge Overpass', which has a waterfront atmosphere.
For those interested in walking across, take the N/R to the City Hall station. You'll find the pedestrian entrance near the eastern side of City Hall.
Related posts: On the Brooklyn Bridge, Fall From Above and More of the Brooklyn Bridge.