The High Bridge has been closed to the public for 40 years (aside from a few tours), but will soon reopen. Very soon: on June 9th. The bridge (which recently got the children's book treatment from Sesame Street’s Maria) spans the Harlem River to connect the area around West 170th Street in the Bronx to the area around West 173rd Street in Manhattan. It's part of the Old Croton Aqueduct, which brought NYC its clean water, and first opened in 1848—some declare it to be "The Original High Line."
The pedestrian bridge (NYC's oldest standing bridge!) will finally reopen on June 9th, about 6 years after anticipated—according to Welcome2theBronx, they have "been building for years for this landmark to reopen and connect the neighborhoods. At over 2,000 feet in length, it isn’t anywhere near as long as the High Line in Manhattan but at almost 140 feet in height it more than towers above the city offering incomparable views."
Bring your bike, or your walking shoes—NYC Parks has a guide of what you can experience around the bridge. And click through for a look back at it, from construction through the 1920s.