When to go
You can photograph the Lower Manhattan Skyline and Brooklyn Bridge from the Manhattan Bridge during any month of the year, as it won't look much different season to season.
This view is best to capture at sunset because the colors light up right behind the skyline. As it gets darker, you'll also be able to photograph the skyline lights as they turn on.
Field tips
There's a chainlink fence along the walkway, but you can normally find a spot where some of it has been cut out to stick you lens through for a clear shot.
This is a great spot to capture with almost any focal length, but for this specific shot, I used a focal length of 55mm. You'll be able to capture the entire scene without compromising the details in the image.
Using a tripod here can be helpful. This side of the bridge is walking only, so you don't have to worry about bikes or other vehicles.
Walk to the other side of the bridge, towards Manhattan, to photograph the view of Brooklyn. Get creative here — there are so many different perspectives you can shoot.
Current weather
Do nearby
Since you're on the Brooklyn side, explore Dumbo. This area is filled with shops, dining options and waterfront views.