En español | Romans call them the Ottobrate romane — the October days. And they are, as any Roman will tell you, the best days of the year to see one of Europe's most ravishing capitals. The city shines with modern-day personality and looks, as well as the history, culture and art that are so much a part of the place. And even more fabulous: So much is absolutely free.

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Take the famous, spectacular Trevi Fountain. You can wander through the mazelike old center of Rome, stand before the fountain and feast your eyes; all this will cost you is the coins you choose to throw (right hand over left shoulder) into the water, just as the actors did in the 1954 film Three Coins in the Fountain.

I never tire of visiting the Spanish Steps, above. Beautiful in their own right, they also provide perches for students, artists, tourists and shoppers, who make for some fine people watching. The bustling Piazza Navona and the gracious, spacious Piazza del Popolo invite leisurely sightseeing. It's even free to enter the nearby Pantheon, still astonishingly well preserved 1,889 years after it was rebuilt by the Roman Emperor Hadrian.

Some things are worth paying for, though — the Vatican Museums, for example. A full ticket costs about $20, but if you book online, you won't have to stand in line. Entry includes a visit to the Sistine Chapel, where you can gaze to your heart's content at Michelangelo's glorious ceiling, then slip away to the basilica and avoid the lines outside its entrance.

Of course, you come to Italy for the food, too, but make an effort to get away from the obvious tourist areas to find the best options at affordable prices. In the immediate vicinity of St. Peter's, for example, your pizza will likely come from a deep freeze. But you have to stroll only a few hundred yards down nearby Borgo Pio to find a decent little trattoria. If you want the taste of traditional Roman cooking, a personal favorite of mine, in the center of town, is Matricianella, at Via del Leone 4.

I look forward to the Ottobrate romane more with every passing year. There may be the odd, brief spell of clouds or rain. But in between come golden days with Goldilocks temperatures: neither too hot nor too cold. And since, by October, every last child has returned to school, grownups have the city to themselves. 

What to Know About Rome

Tipping: Follow the local custom: Romans, if they feel generous, will leave maybe 6 percent. You should do the same.

Sleeping: Noise can be a problem in the city center. But the Hotel Campo de' Fiori is surprisingly quiet and plush.

Hooper is Italy correspondent for The Economist and author of The Italians (2015), a portrait of the country's culture and people. He lives in Rome.

Also of Interest: How to See Europe on a Budget - Barcelona | Paris | Berlin