Miscellaneous: It can be very easy to lost your way in Brooklyn, especially if you’re not familiar with the area and you wander away from the main streets. Hence it’s a good idea to carry a small street map. Though there will always be someone around to point you in the right direction. I took the subway out from Manhattan one Sunday to explore Brooklyn and got completely lost in a Hasidic Jewish neighbourhood. Subway stops are less common out here and I was walking around in circles for ages. I did get to talk to some interesting people who could tell I was lost and gave me directions back to the Subway (after giving me a long, very interesting history of their neighbourhood!)
Walking shoes are needed if you plan on going far. Shopping for shoes once you are in NY is not recommended since they won't be broken in yet and there are way too many choices.
Photo Equipment: Take your camera and film. I like to have a bag that doesn't look like a camera bag. It helps to look less like a tourist.