When you tell people you are going to Alexandria, their eyes light up. “How fabulous,” they breathe, “lucky you.” Everyone, it seems, has a hazy, romantic notion of the place. In the mind’s eye, it is the fabled city, founded by Alexander the Great, for two centuries the cradle of civilisation, second only to Athens as a centre of culture, the pinnacle of Greek imperial might.

For some it is the setting for Lawrence Durrell’s Alexandria Quartet, a cosmopolitan melting pot of clever Jews and louche, expatriate Europeans, painting, writing poetry, gossiping in waterfront coffee houses; of generals planning battles in the desert sands of the Second World War; of the poet Cavafy, writing its history and dreaming of promiscuous, loose-limbed boys and the failure of love. For others, it is the centre of the most thrilling archaeological discovery of our time: statues of Cleopatra, of sphinxes, of great slabs of stone and massive furniture from the Pharos lighthouse.

“The capital of memory”, E. M. Forster called it, and it is as well for every visitor to Alexandria to hold that phrase in his mind. Because memory and imagination in spades is what you need when confronted with the modern city: shabby, concrete high-rises; the six-lane highway snaking along the 20km (12 miles) corniche full of evil smelling yellow taxis, hooting their horns and switching lanes like dodgem cars; the construction sites, half-made roads, broken pavements and shops selling dodgy electrical goods, mobile phones, cut-price leather jackets and household ornaments, all suffering a terminal taste by-pass.

There is nothing left of the ancient city — save the harbour excavations and some ancient catacombs — no theatre or music scene to speak of. The guidebooks urge the visitor to go to a busy intersection at the city centre and stand on the spot which was once the crossroads of the ancient city, the axis of the Canopic Way which led from the Gate of the Sun in the East, to the gate of the Moon in the West, bordered by columns from one end to the other. Stand and weep, more like.

They recommend you drink coffee at the Trianon and stay at the Hotel Cecil to soak up the atmosphere, but the ghosts of Flaubert, Durrell and Forster are long gone and these places are sad affairs. We wanted to stay at the Cecil, thinking it would be splendid in a faded way and rather sexy, like staying at the Algonquin or Raffles. But our tour operator put us in the Sheraton instead.

Good move. This tower block hotel is right at the end of the esplanade, a taxi ride out of the centre, but it has views over a little curve of sandy bay and the gardens of King Farouk’s summer palace (the President’s now, since the revolution) with its palm trees and myrtle hedges and the 60ft (18m) pigeon loft which supplied the King with target practice and fed his prodigious appetite for baked pigeon.

It was lovely walking in the gardens in the early morning (entry about 30p) and strolling down to the beach in the evening when young men set up little stalls roasting tiny corn on the cob or selling paper cones of white beans flavoured with lemon and salt.

The hotel had a luxurious pool completely empty of swimmers (Alexandria’s attempt to market itself as a winter sun destination has yet to take off) and we would repair there after breakfast — delicious salads, freshly made falafels, eggs, fruit and pastries — to read and sunbathe and swim under blue skies and temperatures of around 24C (75F).

Ramadan began while we were there — the streets would empty at 5pm when everyone went home to break their fast — and we became very aware of the deep spiritual meaning it held for people. The young man who brought tea to our room one afternoon stood and talked to us about what it meant to him. “I look forward to it,” he said. “You may not drink or smoke or tell lies or look at ladies; it fills you with peace.”

Another told us: “You are full of energy, you feel healthy and very patient.”

The crowning glory of Alex (perhaps its only glory now) is the library opened last year close to the site of the 3rd-century BC Mouseion — home of the greatest library in the ancient world, a complex of laboratories and conservatories, a zoo and the world’s most important books. The modern Bibliotheca Alexandrina is an elegant construction with a vast, curved roof which filters sunlight down into the 2,000-seat reading room. It has annoyingly arbitrary opening times, so we didn’t spend nearly as much time exploring it as we would have liked, but we did occupy a morning among the wonders of the Rare Book room.

There, encased in glass, are the original books, papyrus and manuscripts, returned from all over the world: The Guiding Light of Kings: An Introduction to Sufism; The Luminous Stars in Praise of the Best of Mankind; The Treatise on Modern Sciences; full of diagrams and scales and astronomical charts, written in 1810.

In the evenings, after a couple of stiff margaritas in the Sheraton cocktail bar (few restaurants serve alcohol), we would go out to eat, choosing our fish from marble slabs and grazing on grilled aubergine and peppers while it was cooked for us. We would finish off with a plate of fabulously fresh peppery rocket leaves.

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