It's your first day at the Edinburgh Festival. You've been smart enough to organise your accommodation well in advance and you're feeling smug about being within walking distance of Edinburgh Castle instead of being stuck at the far end of the A68. Armed with various Festival guides and the hundreds of leaflets thrust at you by panicking young thespians within moments of your arrival, you are sitting in your rented flat ticking off possible shows. So far you've noted Louise Rennison's Sex Tips for Girls, a Bolivian String Quartet, and the latest revelations from a brilliant up-and-coming gay socialist transvestite called Chloe Poems.

You arrived in the city last night, dumped your luggage and headed out with the intention of catching a late show. You fancied a drink first so dropped into Bennet's bar by the King's Theatre, where you fell into conversation with an American academic and a Glaswegian escapologist.

The escapologist reminded you about Rose Street, which you recalled from a visit to the Festival years ago. You remembered the warm, traditional bars and good conversation with local artists and writers, and so the three of you decamped.

It was a bit depressing to find Rose Street well smartened up and with bouncers guarding the pub doors, so you suggested a visit to a bar called Sandy Bells because it was here you first met the great Scottish poet and folk historian, Hamish Henderson, when you were 16. You stood looking at him, in awe of his teeth. But last night wasn't your lucky night, for when you arrived at Sandy Bells it was closing. You were tired anyway, so headed back for an early night, still cultureless.

So, it's now the morning of your first full day at the arts festival to end all arts festivals. An early-morning show? OK, but look, it's sunny and the light is extra sharp and the air smells of burning hops from the brewery. You've known the festival in years when everything has been dreary and drenched in constant rain so you might as well make the best of it. You wander down to Princes Street Gardens - where Princes Street hits Lothian Road.

At this end of the gardens there is a gigantic fountain, a folly or masterpiece depending on your taste, and you sit at a table beside it, with coffee and sandwiches from the mobile cafe and do your best to avoid the wasps that are already droning around the tables and weaving in and out of the numerous wire waste-baskets.

It's so lovely here. The fountain sounds as a fountain should, the thin sunlight is on your face, and in the near distance a band is tuning up for an outside concert.

Noon now. Too late for a morning show. An afternoon show? But you've left all your guides and brochures at home, and really it's far too nice to sit in a cramped little theatre watching a play or tomorrow's hungry contenders for the crowns of French and Saunders. Instead, you amble down to Stockbridge and rummage among the new antique shop till it's time for a light lunch at one of the numerous coffee houses.

By now early afternoon is giving way to late afternoon and you've still to have your first sniff of culture. You decide to walk up to the Assembly Rooms in George Street to see what's on - with 900 performances of numerous shows over three weeks, something's bound to take your fancy. As you set out for your first cultural experience of the 50th Edinburgh Festival you suddenly get an inexplicable urge for shady riverside walks instead, and a few minutes later you are beside the Water of Leith. You walk beneath trees beside a river - a secret valley both moments and light-years away from the hum of festival traffic.

Flowers that have escaped from the cultivated gardens of the grand, leaf- hidden houses above you have rooted here, their colours a bit paler in the gloom, and the last of the summer's dragonflies helicopter about above stepping stones. You find a bench and sit down for a while, and read the last few chapters of the book you started on the long train ride coming up to Scotland.

By now you've missed all the afternoon shows and so you return to your accommodation for a rest and a shower. You doze off and dusk is falling by the time you are back out among the scrum of festival goers. The very last sunbeams are glittering on the tall buildings and spires, but that's fine, for when it sets they'll still retain their beauty. Illuminated by discreet spotlights they'll float in a faint haze and you'll gawp at them in wonder, and wonder why you don't live here year round.

You've wandered through the old part of town and crossed Waverley Bridge into Princes Street again. In the open space around the back of the National Gallery there are jugglers and street musicians and the Glaswegian escapologist. There are also pavement artists and students advertising their shows with an urgency that makes you realise the venue they've booked to perform in is four miles and two bus changes from the city centre. You buy an ice-cream and, browsing among the faces of the multitude, spot the American academic from the bar last night. You were both a bit disappointed that Sandy Bells was closed so decide on a quick visit now.

An ex-pupil of Hamish Henderson is singing a traditional Highland lyric - it's so beautiful you and your American academic forget about theatre. This is the crack. It's theatre enough.

Maybe tomorrow you'll take in a show. Maybe after a visit to the nearby seaside or to the Museum of Childhood, or to the wonderful National Gallery of Modern Art. Or maybe you'll just wander in the ancient courtyards where the ghosts of Scotland's great romantic poets and novelists peer down from narrow, turreted windows. You might even visit the Castle if you've time, or take another slow stroll down the Royal Mile. For by now you are at ease. By now it's dawned on you that you've already bought your first ticket of the Festival. It was the ticket you purchased to travel here, the ticket that got you to the greatest show the Festival can offer, to Edinburgh itself.

Brian Patten joins Willie Russell, Adrian Henri, Roger McGough and Andy Roberts in Words on the Run, a mix of poems, songs and scripts, at the Assembly Rooms, 54 George Street (0131 226 2428) 21-25 August