There is nothing more galling than finding that your colleague has got there before you. In 1899, the poet and Guardian reporter John Black Atkins arrived in Cape Town to cover the Anglo-Boer War.

His shipmates on board the Dunottar Castle had included the advance guard of the Fifth Army Corps and the young Winston Spencer Churchill, correspondent of the Morning Post. Tired from the journey, the two journalists travelled rather despondently up to their hotel in a dilapidated cab "that looked like a London hansom which had received a violent blow on the top".

Yet the hotel, only established that year to accommodate the ever-increasing flow of colonial soldiers and officials who would prosecute that unfortunate episode - the British Empire in Africa - was accounted "a particular star". Alone of the city's hostelries in those days, the Mount Nelson (as it is still called) had style.

As Atkins put it: "I have seen hotels on which far more money has been spent; I have never seen one on which money has been spent to such good purpose. The collection of old prints, the Chippendale chairs, the Persian rugs, were all surprising and admirable." Today, the Mount Nelson is, if anything, more elegant still.

It is luxurious in an old-fashioned (but not stuffy) way, with large rooms and a beautiful situation in seven acres of parkland on the lower slopes of Table Mountain.

The food in its Cape Colony Restaurant is some of the best in the city, the top dishes including smoked crocodile, Jurassic-sized grilled crayfish and the Cape-Malay "Malva Pudding", a mind-blowing, exotic variation on the syrup sponge. After eating there you'll need a walk, and this, too, is laid on pat: a breathtaking avenue of palms leads down to a colonnade gate and, suddenly, you are in the heart of the city, walking through Cape Town's 17th-century Van Riebeeck gardens (with a "scent garden" for the blind) and down to the shops and museums, with their art-deco ironwork and neo-classical facades.

Then, at sunset, back to the Mount Nelson (or the Nellie, as it is affectionately known), its walls painted dusty pink. Some might find the Mount Nelson a bit of a period piece, but anyone with even a fraction of my predecessor's discernment can see that its owner, the Orient Express group's boast - that this is one of the best hotels in the world - is true.

As such, it is quite (but not outrageously) expensive, and can be recommended for a once-in-a-lifetime experience, a honeymoon or a wedding anniversary, and is easily reached from Europe in an overnight flight.

In the old days, travellers used to break ship to stay at Reid's, the Nelson's sister hotel on Madeira, before completing their journey. No doubt the captain would have taken care not to steer into False Bay, so named because ships would run aground there, thinking that they were clearing the Cape.

Arrival today is still dramatic enough. Arrive early in the morning, and you'll see False Bay and the harbour itself, and the sublime Table Mountain towering over all, its tablecloth of cloud matched down on the coast by the surf of two oceans, the Atlantic and Indian.

The city itself turns out to fulfil that double heritage and more, with its range of cultures spanning Indonesia (from where the Dutch brought as slaves the ancestors of the Cape Malays, the city's liveliest inhabitants) and Bombay, Home Counties and High Dutch.

You soon learn that not all of Cape Town is like the Mount Nelson. In fact, very little of it is. As befits a great port, the ocean is very much present in the city, which feels like a cross between Sydney and Miami, with a fair bit of Edwardian and Afrikaner architecture thrown in.

By the waterfront - newly and not very happily developed - are hundreds of nightclubs and restaurants; higher up, the well-guarded, well-gardened mansions of the likes of Mark Thatcher and Charles Spencer.

It is while peering surreptitiously through the gates of these, perhaps, that the dark shadow of apartheid falls over your easeful reflections - you suddenly realise that you haven't felt this place is like Africa because Africa has been kept out for so long. For, while you will see many Cape Malays and Asians in the centre of Cape Town, and a large number of whites dripping in gold, you need to take a trip out to one of the sprawling Cape Flats townships to reinforce the sense that you are in a political hinterland.

Stretching as far as the eye can see, made of cardboard, tin panels and odd bits of plastic at the periphery, and bricks and mortar in the more established, central areas, these shanties are a salutary reminder of South Africa's situation.

They have also become tourist destinations in their own right - along with Robben Island, where Nelson Mandela was held in solitary confinement for much of his 27 years in prison. On the boat trip out to the island, you'll likely as not be tracked by dolphins, their good-humoured mischief - like the newly-painted, sparkling cells - distracting you from the painful political heritage this day-trip describes.

Other tours available to the visitor who is determined to get the best of the sights Cape Town has to offer include a thrilling helicopter ride over Table Mountain (or ride up the newly-restored cableway - much cheaper), a visit to the wine estates of Paarl and Constantia, an outing down Cape Peninsula, and a trip to see whales along the coast.

The latter is well worth doing, offering the easiest land-based whale-watching in the world. Though sightings aren't guaranteed, you'll be unlucky if you don't at least see the distinctive spout of the southern right whale, blowing up vapour.

The truly blessed see whales leaping up ("breaching") from the water, often close to the shore, or playfully waving their V-shaped flukes in the air ("sailing"). At the rustic fishing village of Hermanus, a whale crier with a kelp horn will announce the whereabouts of whales frolicking in the bay.

One of the few disappointments of Cape Town is that you are unlikely to do much frolicking in the bay yourself - the water on the Atlantic (west) coast is far too cold, averaging around 5C, while the warmer, Indian Ocean currents of the east coast are only just about bearable (Fish Hoek and the astounding Long Beach are the best spots).

Another disappointment is the slight air of nervousness about crime, as evinced mainly in jokes about hold-ups in the other great South African city, Johannesburg. Now renamed Gauteng by the post-apartheid administration, this comes out in the quips as the anagram "Getagun".

While Capetonians themselves talk about crime a lot, I felt in no danger walking around the city centre at night - though tourists would be unwise to spend much time after dark in the Cape Flats townships, where the murder rate is said to be higher than even Johannesburg's.

Yet you have to concede that part of the excitement of Cape Town, and indeed the whole country, lies in its collision of natural beauty and socio-political mayhem. Somewhere between the Truth Commission, the spectacular mountain ranges of the Southern Cape and the semi-desert plains of the Karoo, the story of South Africa begins to emerge.

As the Guardian's John Black Atkins put it nearly a century ago: "It is a striking journey through the great tablelands of Cape Colony; the aspect of the country is a singular mixture of gloom and beauty. . . The karoo and the kopjies seize your imagination by the throat at once and compel your mind, but compel it with the power of something mysterious, gargoylish."