Rome wears history as casually as a bauble. Even before I get to the hotel my taxi driver is into a well-rehearsed routine. This, she points out, is the Palatine Hill, there the Circus Maximus, here the Forum. We round the corner and the familiar outline of the Colosseum glides past. You can't argue with the solidity of these forms. They are not Johnny-come-lately Las Vegas attractions bearing similar names. Here, in bricks and marble, are the real palaces of the Caesars. These were fully grown monuments for millennia while the defining landmarks of other cities were still in short trousers.
Rome also has the Spanish Steps, the Trevi Fountain and the Vatican. Its embarrassment of riches has entered popular culture through movies such as Roman Holiday, The Agony and the Ecstasy, Three Coins in the Fountain, La Dolce Vita and Gladiator. Rome exists in our collective memory as a mythical space, but one that can be visited with relative ease. No surprise then that it is the third-most popular city in Europe for tourists, after Paris and London. The challenge for modern visitors is all about finding ways of seeing the Rome of their dreams through the crowds.
Money helps. For instance, €350 buys a "private tour" of the Vatican for two. My guide, James, explains that the Vatican now hosts some four million visitors a year – the volume has quadrupled since the 1980s. It is 8am and we have just negotiated the airport-style security at the cavernous entrance hall. For an hour, we will have privileged access before most of the public are allowed in.
Fantasies of being alone in the Sistine Chapel, however, are soon dispelled. The special access is not quite that exclusive. Coach parties of tourists who have also paid for passes are herded past in a race to be the first to Michelangelo's chapel.
In high season, the atmosphere within can be reminiscent of an echoing municipal bathhouse. The restriction on numbers at this time in the morning does elevate the experience. The mood is semi-reverential. There is a sense of being in the presence of greatness – as if Nelson Mandela had walked into the room. But it is a murky winter day and, because the Vatican authorities don't permit artificial lighting inside the chapel, I still find it difficult to make much of the most famous frescos in the world.
The private tour does deliver a gem in the form of access to the Niccoline Chapel, which is otherwise closed to the public. James ushers me across the mosaic floor in the Room of Constantine (it dates from the third century but the public can tramp all over it) and has a word with a guard. We are discreetly ushered through a small door into the oldest part of the Apostolic Palace. This is a different world. On the far side of the large colonnaded room another small door admits us to the private chapel of Pope Nicholas V. It is tiny but brightly lit by windows in two sides of the tower it is housed in.
The walls are covered in luminous frescos, painted by Fra Angelico between 1447 and 1451, depicting scenes from the lives of St Stephen in the upper tier and St Laurence below. They were cleaned recently and the colours are eye popping. The paintings suggest a delight in rendering perspective and an equal relish in depicting gruesome martyrdom – St Laurence is shown being barbecued alive. We are supervised by the guard but are otherwise alone. These frescos cannot compete with Michelangelo's for grandeur but there is something very moving in being able to experience them much as the pope who commissioned them did.
There is no escaping crowds at the Trevi Fountain. It is the Piccadilly Circus of Rome – one of those strange no-man's-lands in city centres that have been claimed by Homo turisticus. I spot two English guys in town for the Six Nations rugby match. They scratch their chins and one says: "Is that what all the fuss is about, mate?"
The idiotic human statues are here; the souvenir vendors are here and the Japanese tourists are here. The last are well schooled in the visual grammar of the Trevi; they line up to be snapped in front of the fountain chucking a coin over their shoulders. Except they don't. There is no coin. They adopt a freeze frame pose of someone throwing a coin. They are pretending – an experience with no value or meaning.
In Roman Holiday, Audrey Hepburn's character gets her hair cut here during her attempt to escape from the stifling life of a princess. Today, Audrey would take one horrified look and run straight back to her palace.
Cardinal Scipione Borghese built the Villa Borghese as an escape from the hurly burly of Rome. It was a villa suburbana – a party palace – and quite likely the setting for 17th-century antecedents of Signor Berlusconi's bunga bunga extravaganzas. It is now the Gallery Borghese. I make my way there through the surrounding gardens on a crisp morning with snow piled up in decaying heaps; a clear sky sparkles through a canopy of the umbrella pines that characterise the city.
The gallery has just 20 rooms and has opted to deal with overcrowding by selling tickets on a timed-entry basis. The upside of this is that you'll find yourself jostling with only 359 others as you elbow through the extraordinary collection of Berninis and Caravaggios. The downside is that tickets, in summer, sell out days, if not weeks, ahead, which doesn't allow for much flexibility or spontaneity.
There are five two-hour slots during the day and visitors are required to arrive half an hour before their allotted time to collect tickets. I am booked on the 11am shift. There is a melee in the basement level entry hall. The ticket queue and the line for the guardaroba have become entwined. A posse of American blue rinsers from a cruise ship collides physically and culturally with a school outing. Italian children, especially those in a group, are easily the most vocal in Europe. When the teacher unwisely asks them which century the building dates from, the ensuing cacophony is entirely predictable. She limits the damage by making even louder shushing noises.
A narrow spiral staircase leads up to the ground floor where the gallery begins. There is an audible intake of breath as we enter the splendour of Room IV, the Sala degli Imperatori, the villa's second reception salon. The density of decoration is overpowering; every inch of every surface screams for attention. The floor is inlaid marble; the walls are panelled with fine mosaics and the ceiling is frescoed.
Until April, the gallery is hosting an exhibition called I Borghese e l'Antico (The Borghese Family and Antiquity), that sees the (sadly temporary) return of some of the classical statuary that, as the blurb delicately puts it, was "transferred to Paris in 1808". (The incumbent Borghese prince sold the collection under pressure from Napoleon Bonaparte in 1807 while French armies occupied Rome.) Some of the best-known statues are reinstated around the edges of this room – so it takes something special to direct your attention to the centre.
Gian Lorenzo Bernini was only 23 when he completed the Rape of Proserpina but it is an absolute showstopper. Proserpina is fighting off Pluto vainly, her palm crushed into the side of his face, while his massive fingers are indenting her thighs and side. She is clearly distressed, crying out for help, her face dripping with tears. The composition is a whirl of arrested motion, like a split-second exposure caught by a photojournalist. It is scarcely believable that all this human drama has been coaxed out of a massive block of cold marble.
Time is forgotten as I try to cope with the sensory overload of the Borghese collection. By the end of my two hours, I am still on the ground floor, slightly dazed. Most of the 11am crowd has motored on to the galleries upstairs where the Raphaels and some of the Caravaggios reside.
I wander into another room and find myself face to face with Antonio Canova's Venus Victrix (1808). It is an iconic sculpture. I am staring at the nude form of Pauline Bonaparte, sister of Napoleon, who married into the Borghese clan and was the model for this sculpture. But it's not her nakedness that is unsettling. It is the dawning realisation that we are alone. There is no one to chaperone us, not even a gallery attendant.
The spell is not broken when I drift to the next room, which is dominated by another Bernini masterpiece, his extraordinary, dynamic David. Through a connecting door I catch sight of, possibly, the most thrilling piece ever wrought in marble, Bernini's Apollo and Daphne. I feel like Ben Stiller in Night at the Museum. I have the tingling sense of being in a forbidden place witnessing a forbidden scene. Daphne is caught in the moment she is transforming herself into a laurel tree to escape the attention of Apollo. Her skin is turning to bark; her fingers are morphing into delicate leaves that are blowing in the wind. The leaves are like brittle translucent wafers. Bernini is an immature boy show off, saying, "look daddy, this is what I can do with marble".
It is a magical moment. My dream state is interrupted by the public address system announcing the end of the 11am shift.
The gallery is being readied for the next intake. But I have learnt something. When in Rome, sometimes all you have to do is take your time and let the crowds pass you by.
The writer travelled with Kirker Holidays (020-7593 2283; kirkerholidays. com), which offers three nights' B&B at the five-star Hotel Regina Baglioni from £892 per person. The price includes return flights from London, private transfers and a choice of entrance tickets to either the Vatican Museum and Sistine Chapel, or the Villa Borghese. Rome's Fiumicino airport is served by British Airways, Alitalia, easyJet and Jet2. Ciampino airport is served by Ryanair.
Italy with Us (00 39 06 3972 3051; italywithus.com) offers a variety of tours of Italy and specialises in Rome and the Vatican. Vatican tours cost from €50 for a group tour going in before the official opening time up to €275 per person for a small group, exclusive after-hours experience.
Italian State Tourist Board: 020-7408 1254; italiantouristboard.co.uk