FOR her birthday, a friend was given a ticket for an open-top bus tour of Edinburgh. A busman’s holiday, you might think, since she has lived there all her life, and yet she had a great time, enjoying being a tourist in her own city.

The capital is renowned for the excellence of its bus service, quite apart from those offering a guided tour. I used to know the No26 so intimately that even with my eyes closed I could tell by the purring of the engine how close it was to reaching my stop.

Buses, like cars, have a hierarchy: everyday, super-fast and deluxe. Some, like the No30, have yet to get beyond go-cart. It promises to reach somewhere but never seems to. Best of the lot, however, is the No23. It’s the Rolls Royce of the fleet: not because it is any fancier than the rest but because it drives through the heart of Edinburgh, taking in centuries of history and culture.

The route starts in Trinity, by the Firth of Forth. Though never mentioned in estate agents’ brochures, the No23 must elevate the already exalted property prices in this desirable location. It is known as the Trinity Taxi, because locals consider it their personal limo, and my Primary 5 granddaughter frequently takes into town. She bounces on, with her free pass in her Hogwart’s wallet, and finds a window seat. When leaving she graciously calls “Thank you, driver”, like a formidable Morningside matron.

Running from the Forth to within touching distance of the Pentland Hills, the 50-minute journey crosses from the New Town to the Old, proceeding along the backbone of the city until its terminus in the village of Greenbank. If you’re aged 5- 22, or over 60, it transports you for free.

First there’s the Royal Botanic Garden, a luscious haven, where the roar and fumes of traffic fade behind vast canopies of trees. Thereafter the journey continues uphill through the Georgian splendour of the New Town, past terraces and crescents of immaculate, austere tenements. Next it approaches George Street, the city’s most upmarket shopping and socialising district. At this point the skyline is dominated by the spire of The Hub at Castlehill, which is the city’s festival centre. Alongside are the twin towers of the Assembly Hall, otherwise known as New College, over which a statue of John Knox sternly presides. Situated on the grassy Mound, it is the haunt of the General Assembly of the Church of Scotland, as well as a prime festival venue.

At the foot of the Mound lie the Royal Scottish Academy and the National Gallery of Scotland, where you’ll find Raeburn’s Skating Minister and Landseer’s The Monarch of the Glen. Uphill, beyond them, is Edinburgh Castle. It has lost none of its menace down the years, as it lours over Princes Street. But for some visitors an even greater attraction is the robot lawnmower which nibbles on the Mound’s turf 24/7, like a hyperactive rabbit.

By now, if the bus were human, it would be puffing. Turning the corner past the Bank Museum and the Writers’ Museum, it crawls towards George IV Bridge. I’ve spent years of my life in this rather dour-looking street. This is where the Soviet-looking National Library of Scotland is located, whose reading rooms have been a haven since my student days. Directly opposite is Edinburgh Central Library, where one summer I worked in the accessions department, several floors below ground level. A step away is winding Victoria Street, scene of a million selfies. It leads to the tourist honeypot of the Grassmarket, with its taverns, gift shops and eateries, and memories of the capital’s gibbet.

Don’t forget to get off at the library stop, even if your destination is the National Museum of Scotland. I was too slow clambering downstairs the other day, and was carried far beyond the bridge to the railings of the former Edinburgh Royal Infirmary. Now converted from cavernous wards into Quarter Mile, a chichi residential area overlooking the Meadows, this is the place to draw breath and find al fresco entertainments. If it’s liquid refreshment you require, then Sandy Bell’s bar is close by, the former watering hole of the poets Norman MacCaig and Hamish Henderson, who would occupy opposite ends of the gantry.

But to retrace our steps to the National Museum. Not enough can be said in praise of this astonishing collection, where you could immerse yourself for a week and still not exhaust its treasures. If time is required to digest everything you’ve found there, then climb aboard again, and enjoy the scene as the route takes you to Edinburgh College of Art – the site of the Edinburgh International Book Festival – and past the olde-worlde Cameo Cinema into Bruntsfield.

Overlooking Bruntsfield Links, this is the birthplace of Muriel Spark. More recently it was dubbed the literary quarter of the city, when JK Rowling, Ian Rankin and Alexander McCall Smith were neighbours, though two of them have since changed postcode. A mile further on, as the No23 rolls into Morningside, another claim to fictional fame is to be found.

This bijou, middle-class area was once famed for its bourgeoisie, who reached for a fur coat where the rest of us put on a vest. They were notoriously parsimonious, since Morningside Library was once listed in the Guinness Book of Records as the busiest public library in the world. Reading weekend reviews in The Scotsman, Morningsiders would race to be first in the queue to place their orders when the library opened on Monday, rather than cough up for new books.

This sought-after part of the city is home to Maisie the Cat, the gung-ho heroine of Aileen Paterson’s picture books. Like any self-respecting Edinburgher, Maisie went everywhere by bus. If she hopped onto the No. 23 at this point, it wouldn’t be long before she was within sight of the Pentlands, described by Robert Louis Stevenson as “the hills of home”.

Reaching its terminus, the Trinity Taxi takes a breather before turning tail and beginning its return leg. With such a wealth of antiquity, arts and culture along the way, surely it is the best urban bus route in the world? I’d certainly like to hear of any that can trump what deserves to be called an Edinburgh Festival on wheels.