Best to do this during sunset. When you make it to (or back to) the Brooklyn side check out the neighborhood of DUMBO. When you make it to (or back to) the Manhattan side, check out Battery Park, Oculus, South Street Seaport, or if you have enough energy, take the Staten Island Ferry or visit Hudson River Park Pier 25. If you want to kill two birds with one stone, it's best to only walk halfway and turn around so you get to experience the greatness on either side of the East River. Pedestrian entrance by City Hall in Manhattan and the intersection of Tillary Street and Adam's Street in Brooklyn. Tips: Bring a sweater as it can get pretty chilly up there, I've been told.
Can't wait to do this with the children when they are older and I don't have to push a stroller!