Emerge from a narrow side street and there is the Trevi Fountain, all Baroque plumes of water and leaping horses. Cross a street and there are the Spanish Steps, the Pantheon, the Colosseum, the Vatican. Rome seems to have grabbed all the must-see tourist icons for itself and packed them into a walkable buzz of a city. The centuries have also afforded Rome a healthy number of cafés and restaurants from which to watch the world go by. People watching as much as monument watching is an excellent way to spend time here.

Rome has been a tourist destination for as long as there have been tourists, attracting artists, diplomats, scholars and artists. By the 18th and early 19th centuries, the idle European rich came to gaze at its ancient sculptures and prized paintings before taking large crates of them home to hang in their country houses.

It is fitting that a city so steeped in history should have had a mythical start in life. It was founded in 753BC on the left bank of the River Tiber by Romulus and Remus, abandoned twins who were suckled by a she-wolf. Having killed his brother in a quarrel, Romulus ruled Rome until it was taken over by the Etruscans, among whose kings was the fabulously named Tarquinius Superbus.

As the Roman republic came into being, ordered rule under the charge of elected consuls meant that Rome could develop as a sophisticated capital, with temples, seats of government and fine villas. During the tumultuous decades around 73BC, which saw the revolt of the slave Spartacus, and Ceasar’s assassination in 44BC, the Roman Republic ceased to function. Augustus took control of the embattled factionsand, over the course of his 45-year rule, laid the foundations of the Roman Empire.

It is one of the marvels of Rome that so much of what we see today has survived from the years of the Empire. In fact, unless you have superhuman stamina, it’s best to ration out a few sites a day, making time for that all-important espresso, ice cream or pizza stop along the way.

In terms of presence, you can’t really miss the Colosseum and the nearby Capitol and Forum. Construction of the Colosseum began in 72AD, and to celebrate its official opening in 80AD, 5,000 animals were slaughtered over the course of the 100-day games. Even now, standing in the centre of the arena, with the seats rising in tiers around you, you can half imagine the roar of the crowd and the terror as you waited for the trap doors to release whatever beast was going to try and kill you.

In contrast, the Capitol and Forum were the focus of political and religious life, and are still full of the ruins of temples, grandiose arches and churches. The precious and delicate sculptures and wall decorations from these sites are now mainly on display in the Capitoline Museum, in Piazza del Campidoglio. Also worth a visit are the three sites that make up the Museo Nazionale Romano. Between them, they contain haughty busts of Roman emperors, classical sculpture, exquisite friezes and fragments of wall paintings, which give an intimate glimpse of domestic life in ancient Rome.

Few tourist sites are isolated destinations; many you just come across as you wander the grand boulevards and narrow alleyways that thread through the centro storico. A perfect area to start is the Tritone, roughly the area around the Spanish Steps, Piazza del Popolo and via Ripetta. Starting in Piazza del Popolo on the edge of the sprawling gardens of the Villa Borghese, meander down to the Piazza di Spagna and the Spanish Steps. The steps themselves are a constant parade of passers-by, fanning out to explore and take photos of each other. Making your way south, a shortish walk takes you to the Trevi Fountain. Neptune surveys the scene as mythic horses rear above the cascades in what is arguably the most spectacular fountain in Rome, and which seems only just to fit inside the boundaries of the piazza. To ensure your health and happiness, throw a coin into the fountain backwards over your shoulder.

Head south-west from there and you come to the Pantheon, still an amazing feat of architecture, and all the more extraordinary because the dome, built some 2,000 years ago, remained the largest in the world until the beginning of the 20th century.

The list of must-see sites in Rome could keep you marching for weeks – the Vatican itself, with the epic interior of St Peter’s and Michelangelo’s Sistine Chapel can take a whole day. But racing about on a tight schedule is not the Roman way. Lunch, window-shopping, taking your time over a coffee outside a café is the order of the day.

Rome might not be the heavyweight fashion centre that Milan is, but a stroll along via Condotti , via Borgognona or via Frattina will take you past Gucci, Prada, Dolce & Gabbana, Armani, Valentino and Laura Biagiotti among others. There are also outlets near Rome where you can pick up designer brands for a fraction of the original price. Castel Romano has around 110 boutiques including Cavalli, Zegna, La Perla and Burberry, while Valmontone boasts around 200 designers such as Bottega Veneta, Frette and Byblos and is accessible by shuttle bus.

Via del Corso, one of the main arteries through the city, has major brands and department stores, but if you head north of the Vatican to via Cola di Rienzo you will find similar shoe and clothes shops in a less touristy, more local atmosphere.

No one should miss the flower and vegetable market in Campo dei Fiori, one of the most characterful piazzas in Rome. The Mercato di Testaccio may be where Roman housewives tend to buy their food, but the Campo dei Fiori is the more picturesque market. As evening draws in, the bars and restaurants around it fill up with an arty young crowd.

Eating out in Rome is a constantly evolving experience, with new restaurants such as Primo and Antico Arco leading the way with light, innovative flavours and the finest, freshest ingredients. They are a step away from more traditional Roman food, which focuses on what were poor man’s ingredients: offal, oxtail, pigs’ cheeks, tripe and so on. Spaghetti all’ amatriciana is a classic dish of tomatoes, pork cheek, onion and pecorino cheese. Another, pajata, is not for the fainthearted, being veal’s intestines cooked with the mother’s milk still inside them.

It’s easier on the stomach perhaps to head to Gelato di San Crispino for what is generally acknowledged to be the best ice cream in Rome. Everything is made on site with seasonal fruit, crunchy meringue, hazelnuts and pistachio.

One of the best times to see Rome is during the spring, when the days are already warm, the trees are in blossom and the tourists have yet to arrive en masse. You could drown in tourist literature before you go, but an easier way to get a feel for the beauty, chaos and romance of the place would simply be to watch Roman Holiday. As Audrey Hepburn, as Princess Ann, says at the end of the film, “I will cherish my visit here in memory as long as I live.”