Mini-break Grand Tourers, their feet aching and their craving for the glories of ancient Rome ebbing (and with another three more archaeology sites and two museums to fit in before prosecco time) might feel a sneaky admiration for Alexander, fourth Duke of Gordon, patron saint of slacker cultural tourists everywhere. In the 18th century the Grand Tour was de rigueur for any gentleman of means, yet in 1764 Gordon "visited" all the main Roman sights without leaving his luxurious carriage.

Budget airlines may have made it more accessible for a long weekend, but Rome can still be hard work for the modern tourist. One popular guide suggests "The Ancient City in a Day", a trudge taking in seven sites, six churches and about 5,000 marble steps - likely to leave the most ardent pilgrim gasping for mercy. The archaeologist Mortimer Wheeler once groaned: "What a city Rome would be, were it not for its ruins!"

Much of the historic heart of today's city would be perfectly familiar to the Grand Tourists, though sheep then grazed in the Forum, and the Colosseum was a small farm, with exotic plants said to have sprung from seeds carried in the dung of the fabulous animals imported by the Romans for the games. Some of the most familiar streetscapes, including the Spanish Steps, were created to impress these foreigners. The grandest would have stayed in loaned or rented palaces, bringing their own staff and cooks with them.

Present day visitors can still experience the accommodation of more modest 18th-century tourists, in the Landmark Trust apartment in the building flanking the Spanish Steps where Keats died, and in the poignant museum housed in the rooms where he spent his last winter, his lungs rotting, too ill to enjoy the glories only a stone's throw from his narrow bed. A handful of restaurants and hotels survive from that date, including the Hotel d'Inghilterra, renamed in honour of its English guests, and the Sole al Pantheon, which dates all the way back to 1467.

The tour became steadily less grand into the 20th century, as another institution at the opposite side of the steps pitched at the peculiar British tourists illustrates: Babington's English Tea Rooms (babingtons.net), established in 1893, is still there and still serving excellent tea at eye-watering prices.

In the 18th century the whole process must have been excruciating even for those rare birds who emerged from the British education system genuinely mad for the classics.

The full round of the tour took months, and many of those who survived it - and some who didn't, including a young wife who was already dead by the time her portrait was painted, and the pale young Humphrey Morice, governor of the Bank of England, who only lasted a few years after returning to England - can now be seen on the walls of the National Gallery, in a new exhibition of the work of Pompeo Batoni, the most famous Roman painter of his day.

It was the gap year for aristocratic lads. Several young blades grabbed their allowance and vanished for years on end, improving their minds far from the prying gaze of parents and guardians. But it certainly wasn't all fun and games. Journals and letters home record moans about being ripped off by ostlers and inn-keepers, tailors and border guards, brigands and landladies, as tourers struggled across Europe, the wheels falling off their coaches on the mountain passes and their skin itching from bedbugs, never able to get a nice cup of tea or a proper piece of toast.

Then, when they finally reached Rome, having already taken in Florence, Naples and hauled themselves up the slopes of Vesuvius, there was a stern checklist of great art to get through. Their predecessors left detailed instructions on how to confront these wonders.

Johann Winckelmann, credited as the first modern art historian, who spent years working in Rome, set the standard. Gazing on the Apollo Belvedere, now in the sculpture courtyard of the Vatican museum - created as a temple of ancient art especially for the Grand Tourists - he wrote "before this miracle of art I forgot the entire universe . . . from admiration I pass to ecstasy." (Winckelmann also had an eye for a nicely muscled male torso, and was eventually murdered after inviting the wrong handsome young man back to his rooms to admire his art collection.)

Others were moved to tears, or swooned before the sweet calm of a head of Minerva, or the stupendously muscled Belvedere Torso. One traveller wrote anxiously that he could feel nothing, and wondered what on earth was wrong with him.

Having wept and swooned, they went on to buy reproductions from specialist workshops, in plaster or marble, at everything from desktop to Angel-of-the-North scale: the exiled gods and nymphs still stand forlornly in many a draughty English hall or soggy pasture. Then they went to a painter like Batoni, and to prove they had truly Grand Toured had the monuments included as set dressing in their portraits. Batoni charged by size and elaboration: so much for just a head of Minerva, very much more for every serpentine coil of the Laocon. The National Gallery has a whole room full of his very grandest patrons, painted at barn-door scale: young Thomas Dundas clearly paid the absolute top whack and has half the relics of Imperial Rome scattered around him, even the fountain from which his dog is lapping.

So in 1764 young Alexander Gordon had to do Rome, but he didn't have to like it. He hired the top man, Winckelmann himself, to show him round. They set off in his luxurious travelling carriage, trundling past the Forum, the Colosseum, the Arch of Constantine, the Pantheon, the baths of Caracalla, Winckelmann no doubt lecturing him every inch of the way as Gordon reclined on his cushions. They came to the broad sweep of steps leading up to the Capitoline museum (where Batoni's career began when a passing cardinal spotted a young man drawing beautiful pictures of the sculptures), and the Piazza del Campidoglio (designed by Michelangelo to frame the monumental equestrian statue of Marcus Aurelius). Winckelmann must have stretched an arm with a gesture borrowed from the Apollo Belvedere to indicate the wonders that awaited the duke, just a stroll up the steps. Gordon flatly refused to get out of the carriage - then or at any point in the day.

He surrendered to convention sufficiently to go to Batoni and he's there in the exhibition, gun in one hand, horse in the other, faithful hounds capering around him, knee deep in slaughtered game - not a Diana or an Apollo in sight. However, the curators believe Batoni had the last laugh. The artist took Gordon's elegant pose, one arm raised, body turned, head gazing towards the right, straight from a life-size statue of a hunter excavated only a few years earlier. Ancient Rome got Gordon in the end. It does everyone.

· The Piazza di Spagna apartment, in the building where Keats died, sleeps four and costs from £274 per night (01628 825925, landmarktrust.org.uk).

The 16th-century converted palazzo Casa Banzo (0039 06 683 3909) is next to the Campo dei Fiori in the historic centre. Doubles from€100.

· The Pompeo Batoni exhibition at the National Gallery, London, runs until May 18. Book tickets on 0870 906 3891, nationalgallery.co.uk.