The Water of Leith is Edinburgh's secret spine: a wooded river that runs right through the city in a green slot most people never drop into. This is the best stretch of it — from Telford's aqueduct at Slateford down to Stockbridge, taking in the Modern Art galleries, Dean Village, and a mineral-spring temple on the way.
Start under the Slateford Aqueduct, where the Union Canal crosses the river on a row of 1822 arches, and pick up the walkway below. The path follows the water downstream through trees and over weirs, the traffic dropping away until you'd swear you'd left the city. Climb up to the two Modern Art buildings above Belford — free, with a Landform earthwork on the lawn — then rejoin the river for the drop into Dean Village.
This is the showpiece: an old milling hamlet wedged in a gorge, the weir roaring, the granaries turned to flats. Carry on past St Bernard's Well, a 1789 temple over a spring Edinburgh once thought medicinal, and the river delivers you into Stockbridge — bookshops, a market, pubs on the water. Come up off the walkway and find a table.