In May, I went to the Brooklyn Bridge as part of the 125th anniversary of the construction of the bridge. The bridge is fun to walk across and a relatively easy walk, although I do suggest bringing water on sunny/hot days. The Brooklyn Bridge is an amazing piece of architecture and engineering. Designed like a Gothic cathedral, its construction ended in 1883. To get to the Manhattan side you can take the 4 or 5 train from Franklin Av. to the Brooklyn Bridge-City Hall stop and you will be right there; to get the Brooklyn side take the 2 or 3 train from Franklin Av. to the Clark Street station walk down Clark St. to Cadman Plaza West, turning left onto Tillary St. and left again on Brooklyn Bridge Blvd.
Here are some of the pictures I took(click to enlarge and see a description):