This is the walk you take someone on their first morning in the city: out over the Brooklyn Bridge on the raised wooden promenade, the cables fanning overhead and the skyline you're leaving behind your shoulder.
Start near City Hall and go early — by mid-morning the span is a slow river of people. Stop at the first tower, then mid-span, then turn round; the view back to Lower Manhattan is the one you'll remember. Come down into DUMBO and find the Washington Street spot where the cobbles run uphill and the Manhattan Bridge frames the Empire State Building inside its arch. You'll be sharing it with a dozen cameras. From there it's downhill to Brooklyn Bridge Park, the old industrial waterfront turned to lawns and piers.
Walk the shoreline path to Jane's Carousel, a 1922 machine in a glass box at the water's edge, and end at the Fulton Ferry Landing under the bridge. Take the NYC Ferry back across the water, or walk inland to the F at York St.