A river runs through it

Great cities frequently boast great rivers; that's usually why they became great cities in the first place. The Seine; the Hudson; the Mersey; the Thames and the Tyne. You can name those cities in one, correct? With the Water of Leith it's trickier. Try a straw poll and see how many people believe it's (a) an overpriced Scots version of Evian; (b) an underrated medical complaint; (c) a euphemism for a particularly lethal single malt. The correct answer, of course, is none of the above. The Water of Leith is a short, sharp and straggly river that descends from from the Pentland Hills to perform a neat bypass operation around the centre of Edinburgh. In August, the Festival sucks in artists like a Hollywood audition, and the Fringe draws tourists like a cultural Disneyland. But the river that carves a languid course through the Scottish capital remains a backwater.

Considerable energy has been expended on making the waterside walk a feasible and, often, pleasing experience. A day is needed to make the most of the 14-mile meander, allowing for the odd detour. But if you wish to expend no more than the energy required to get to Leith - a brisk half-hour hike from Waverley station down Leith Walk - you will be rewarded with a port of call recently revived. The street names point to an illustrious history: Cadiz, Elbe and Baltic in quick succession.

The bleak housing estates look like locations for Trainspotting, which is exactly what they are. The dockside, though, has been transformed in the manner of the late 1990s, from post-industrial dereliction to post- modern chic. Britannia waives the rule that old ships never die, they are summararily scrapped. The former Royal Yacht, now a visitor attraction, might attract a few more tourists were she moored closer to the old port rather than being a windswept walk away.

A much more convenient venue to partake in that regal gin and tonic is the quayside Seamen's Mission, which has become the latest addition to the Malmaison hotel chain. You need not be too rich nor clad exclusively in black to enjoy a pounds 12.95 lunch. The start of the walk along the Water of Leith lies across the cobbles and the austerely handsome iron bridge. The first couple of miles are minimal fun, threading through Trainspottingville. "Three traffic cones and a supermarket trolley" reads my first assessment of the waterway's appeal.

Death provides a welcome escape. At St Mark's Bridge, pause to explore the lovely old Warriston Cemetery. Shortly afterwards, you pass Lady Haig's poppy factory, intended to provide employment to those who survived her husband's tactics in the First World War. The Water of Leith gave plenty of jobs to a city which attained self-belief two centuries ago. It fuelled a modest, localised Industrial Revolution - of which more evidence lies upstream - and enabled the builders of Edinburgh's New Town to transport the stone necessary to ennoble the city.

The hauliers' first job was to negotiate a sharp turn to the west, which now parallels the southern border of the Royal Botanic Gardens. Like Kew, these greenhouses and pleasant lawns provide a refreshing alternative to the fumes of the city, but Edinburgh's version is so close in that the city skyline feels within touching distance. The Glasshouse Experience takes you a step further away, with tropical and desert environments beneath a single crystalline roof.

Neighbouring Stockbridge was named after the river crossing used by the cattle drovers en route to Leith, but gentrification has made it more synonymous with Pizza Express (whose premises here boast a clocktower) than with Aberdeen Angus. Now you start the most dramatic part of the walk. The Water is funnelled through a deep channel, which provided power for milling and wealth for the provider of the waterway's folly, a rotunda protecting a woman and serpent.

As you cut through Dean Village, you encounter old millstones that tell the story of the river as a going concern. If you climb to the level of the surrounding landscape, you should emerge close to the Dean Gallery: since March this year, a dramatic, exciting addition to the city's artistic repertoire. Once a hospital for orphans, the neo-classical facade has also served as a nurses' home. It stands opposite the Scottish Gallery of Modern Art, and functions as the repository of everything that questions conventional wisdom.

Once you get past the giant robot that is the sole occupant of the Great Hall, you stumble upon the gift of a large body of work by Sir Eduardo Paolozzi which makes you feel you have trespassed into his studio, and mind. Magritte, Picasso and Dali are among the other angry old men represented.

Your progress back to the Water will be impeded by barriers of a functionalist nature, ie, deadlocked gates. The best plan is to ask for directions to Murrayfield rugby stadium, a slab of Twickenham transported to EH12. Or grab a cab past some carpet warehouse ghastliness to the Tickled Trout pub on Lanark Road. Providing you can track down the path from the pub car park, you are rewarded with a complete change of tone.

From here you progress along a broad, wooded valley that begins as Craiglockart Dell and takes you dodging along a steep-sided path. At the first opportunity, cross the water to make smoother progress along the line of a former railway. Barely half a century ago, this was an industrial artery; just after you emerge from an ill-lit tunnel beneath an outcrop, you find yourself in Colinton, where Scott's Porridge Oats were milled until 1947.

Three miles remain, but they are arguably the most pleasant. After you cross the river once more, the Water of Leith seems to abandon the City of Edinburgh (or is it the other way around?) and plunges into pasture. The town of Balerno is not the end of the Water, but following the trail any further gets tricky as the river diminishes to a stream. As a piece of advice to hikers and festival participants alike, the following is apt: quit while you're ahead and get the bus back right now.