The whole month (or even a year) would not be enough to do justice to the city. Self-control is essential. Restrict sightseeing to one of everything - basilica, chapel, church, piazza and bar. You will have to make an exception for countries: the walls of the Vatican City encircle the smallest nation in the world.
If influence-per-square-inch could be computed, the 108 acres of the Vatican would make Japan seem insignificant. And it is a world-beater as far as churches are concerned: it contains the world's largest.
The curving colonnades of St Peter's Square reach out to embrace you, and draw you into the basilica. The fierce white facade is overwhelming: you do not walk into the body of the church so much as creep in, cowed by the arrogance of space above and around you.
The only way to get a grip on St Peter's is to scale it. A series of 628 steps hauls you to the top of what, predictably enough, is the world's biggest dome. Rome looks manageable, almost mundane, compared with the audacity of the construction from which you peer precariously. The facade is topped with statues of Christ and the Apostles, clutching crosses which make them look uncannily like a rock band.
Put away such sacrilegious thoughts: the Sistine Chapel shows vividly the fate of those whom St Peter rejects from the Kingdom of Heaven. Michelangelo's message is made clearer by the clean-up completed earlier this summer. Now we can enjoy the vision of hell in all its intensity.
But first you have to get there. The chapel opens for only four hours a day, and for every one of those 240 minutes a consignment of visitors pours in. It is at the end of a bewildering walk through the Vatican Museum, where the tastes of successive pontiffs are exhibited. Primed by a thousand works of religious art, you might imagine the moment of entering the chapel to be an instant of bliss. In fact, it is ghastly.
Anyone who misses the heaving masses on old-style football terraces should head for the Sistine Chapel. A thousand or more people cram themselves into it, doing their best to break all its rules. 'Achtung]' barks a recorded announcement, before reminding visitors in four languages that they should not speak, take photographs using flash or make video recordings. You can hardly hear the instructions for the whirr of camera motors and whine of recharging flash units.
There is a simple strategy to adopt. Wait (quietly) on the bench at the back until everyone leaves. At 1.30pm the crowd melts noisily away and you have a reverential 10 minutes before the warders exercise the only real power they possess, of ejecting stragglers.
Over four years, Michelangelo told the story of the Creation in a series of increasingly miraculous panels. High Renaissance slips into Mannerism above the altar, with the Last Judgement. The single most harrowing image is of St Bartholomew, who was flayed alive, holding his skin. It is said that Michelangelo wanted to reflect his own pain at having to undertake the papal commission, and painted a portrait of himself as an old man on the dangling human skin.
Other places boast of possessing as many pubs as there are days in the year. Rome seems to have as many churches as there are saints. Placed in any other city, many of them would be richly celebrated. However, few of them bear comparison with the mighty St Peter's.
They do themselves no favours by being almost universally pig-ugly from the outside. The sort of urban grime normally associated with industrial excess has besmeared itself upon church walls whose blankness belies the wealth of the contents. Sant' Andrea al Quirinale is a prime offender, its filthy exterior concealing a baroque feast by Bernini.
From here it is no more than a stumble to the Spanish Steps or the Trevi fountain - if you truly want to reacquaint yourself with the people you shared the Sistine Chapel with. But to meet the few remaining Romans, go elsewhere: the Piazza Navona. If there is such a thing as a classic square in a place as architecturally chaotic as Rome, then it is here. A minor palazzo or two, a heavily disguised church and a ring of restaurants providing the setting for promenading citizens.
Ordering anything on the terrace of a cafe in the centre of any of Italy's big cities is roughly the equivalent of opening your wallet and asking the waiter to help himself. At the Caffe di Colombia, which has the best pitch on the Piazza Navona, brace yourself for bankruptcy and ask for a beer. But not only does pounds 4 buy a glass of Peroni, it also rents you a prime position. Then, instead of fretting about the lire-per-litre cost of your beer, exchange such arithmetical irrelevances for contemplating a piece of geometric precision, located exactly 20 miles north-west of the capital.
Mathematically, Lake Bracciano is probably the most perfect place in the world. The lake's shoreline is a strict circle, the result of the volcanic eruption which created it. Further analysis with a protractor reveals that the lakeside towns of Anguillara, Bracciano and Trevignano are perched at 120-degree angles from each other.
For a place which is technically so perfect, Lake Bracciano is tricky to reach. You have to catch a doddery diesel train from an obscure station on the outskirts of Rome. It rumbles along a single-track line, pausing at ill-kempt stations to allow inbound services to squeeze past. Finally it creaks into Anguillara, or at least a platform whose faded boards bear that name. The town, and lake, turn out to be a three-mile walk along a dusty road which appears to function as a training track for Rome's scooterati, who rev their Vespas and test their skills of narrow avoidance on hapless hikers.
You forgive them, and the heat, when the road reaches Anguillara proper. It gives a final twist and spills you out on to the lake; clear, fresh and cool. The surface trembles in the breeze, scattering sunlight on the graceful pines which fringe it and the jolly bathers who disrupt it.
Before Lake Bracciano became a summer bolthole for Romans, Anguillara was a fishing village. The boats are now hopelessly outnumbered by pedalos (propelled as recklessly as the average scooter), but the ambience of the ancient streets is untainted. One feature, though, looks curiously out of place: the huge stone archway presiding over the entrance to the old town, supporting a clock which makes up in size for what it lacks in punctuality.
The reason for its existence is simple civic rivalry. In Anguillara, I met a man from Trevignano. First he jabbed at the map: 'Dodice-dodice-dodice,' he said, indicating that the three lakeside towns are exactly 12 kilometres (seven miles) from each other. Then he declared his home town was the apex of the three, and insisted on taking me there.
He demonstrated that the 120 degrees to Trevignano can be covered in dodice minutes if you put your foot down, and deposited me in the town square, the site of an archway and clock several notches more grandiose than the one down the road.
Once the dust raised by my departing driver had settled, little disturbed the afternoon calm except the high-spirited jabber of a benchful of widows. Presumably these women are subsidised by the town authorities to beautify the place and bid 'buona sera' to visitors. They also dispense directions on how to reach the monte above Trevignano. The inaccuracy of these instructions reinforces the impression that the widows have not made the climb recently. So you battle with barbed wire and brambles to reach the remains of a church at the summit. A few scratches do not deflect from the view: lazy folds of hillside diving into the shimmering lake.
Trevignano has more than the best panorama and the cutest senior citizens: it also has a fine beach. The town does a good line in beachside cafes, too; but the life-expectancy of the staff must be short. To take a tray of beers out to idlers drinking the afternoon away, waiters have to dodge the motorists hurtling along the main road.
The final dodice-kilometre climb to the town of Bracciano terminates with a flourish at the gates of the Orsini castle. The Orsini family built their private stronghold five centuries ago, on the ruins of a medieval fortress. The steps leading to the top of the tower take you to the highest point overlooking Lake Bracciano, the very picture of precision.
Getting there: The lowest fares between the UK and Italy are available through discount agencies such as Multitours (071-931 7787), from whom a London-Rome flight on Alitalia, for example, costs pounds 235.
From 13 September, the British Airways (0345 222111) fare from Heathrow falls to pounds 173, and in November BA is charging only pounds 99 - its lowest price for 12 years.
These flights serve Fiumicino airport, from where there is an hourly non-stop train to Rome's main station, price 12,000 lire ( pounds 4.80).
Getting around: The flat fare on Rome's buses is 1,200 lire (48p); the ticket allows a transfer and remains valid for 90 minutes. Trains to Anguillara and Bracciano leave approximately hourly from Ostiense station in the south of Rome, fare 3,900 lire ( pounds 1.60).
Accommodation: Simon Calder stayed at the Albergo Pomezia, in the centre of the city at via dei Chiavari 12 (010 39 6 686 1371), which costs 70,000 lire ( pounds 28) single, 90,000 lire ( pounds 36) double.
Recommended reading: The Eyewitness Guide to Rome (Dorling Kindersley, pounds 14.99).
Further information: Italian State Tourist Office, 1 Princes Street, London W1R 8AY (071-408 1254).
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