You notice the difference as soon as you cross the Tiber. Rome is ancient. Trastevere - literally 'across the Tiber' - is elderly, certainly, but with a nonchalance that contrasts sharply with the swagger you will often find in Rome proper.

For this is the real Rome, the locals say. Here the original language is spoken. Here, if you are lucky, you might catch sight of an old woman leaning out of a fourth floor window, carefully lowering a bucket to the pavement so it can be filled with fruit and vegetables. Or flowers. Or sausages. Anything to save her the long climb up those cramped stairs.

I pinched myself in Trastevere. For a moment it seemed we had slipped countries. I sensed Paris. Perhaps it is because finally here there are streetside trees, a notable lack in the rest of this great stone city. Romans love gardens - Italians are some of the world's great gardeners - but local city planning forgets them. There are spacious piazzas and squares, but few trees or even grass are seen in public in central Rome. Of course you catch glimpses inside villa courtyards, off the street. I even saw a palm tree flourishing in one. But here, in Trastevere, they have found a way to create lush gardens that become safe and private outdoor living and respite from the heat. Once you know to look up there, you see leaves and branches sprouting everywhere from the rooftops, a green clue to their hidden charms.

There is a relaxed air to this village-within-a-city. A gypsy girl cadged around us as we walked through one square; amateur artists tried to capture the essence of the first Christian church in Rome, the third-century Santa Maria in Trastevere, on canvas; and a mound of oranges glowed outside a restaurant where the waiters were setting out chairs and tables in the sunshine. At another cafe, newspapers half hid the tiny tables, and the smell  of irresistibly good coffee drew us in.

Trastevere was originally peopled by sailors from Ravenna. These strong men were needed to work the giant awning on the Colosseum. Tradesmen followed - tanners and potters, millers and furniture makers. Then artists and whores. Today the place is full of piazette., open areas too small to qualify as piazzas, churches, gardens, restaurants (some serving authentic Roman food), bars and cafes, and a 'Left Bank' ambience hangs in the air.

Raphael was a fan of this neighbourhood. He courted the baker's daughter here, and at the Villa Farnesina you will see some of his frescos. From the Piazza Garibaldi, where there have been gardens from Caesar's times, you will get one of the best views of Rome. The original wild Italian grape grows only here, no doubt part of the stock from Imperial times, when this whole area was the centre of a large wine industry. The local tongue persists too, with some older people still refusing to speak Italian, preferring pure Roman as their language.

Ask a dozen people who have visited Rome 'Have you been to Trastevere?' Chances are most will say no, yet it is a comfortable twenty-minute walk down the riverside from the Vatican and hardly more from the Colosseum. The streets are jumbled, but green havens around various massive villas give it space.

Make sure you pass across Isola Tiberina on your way to or from Trastevere. This doll-sized island in the Tiber is linked by the Ponte Fabricio and Ponte Cestio to either bank. It was here that a miracle-dispensing snake, meant to save Rome from plague, jumped ship in the third century BC, so it was appropriate that almost two thousand years later Portuguese monks established the Ospedale Fatebenefratelli there. The buildings almost fill the island, but steps lead down  to the embankment on the Trastevere side, making an ideal romantic spot to stroll or relax.

Trastevere doesn't have any ancient Roman ruins. Perhaps it doesn't need broken reminders of Rome's past. This place, preserved in time, simply gives visitors another perspective, offers a fresh green view. And great coffee!