I have heard there is still black magic in the Seychelles — “We call it grigri,” intones the waitress with the tight Afro curls, as I dissect my red snapper on the island of Mahé. She stares into the middle distance and shifts her weight from foot to foot. Behind her, waves lap on buxom granite boulders. “I have only heard this, of course,” she insists, adjusting her blue skirt and tugging uneasily on her T-shirt.

On my first day in Kigali, I had lunch on the veranda of the Banana hotel, eating perfect grilled fresh fish from Lake Kivu.

The horrors of the 1994 genocide weave into every part of life here in Rwanda, and before long, the glamorous owner, Françoise, confided that, on her return to Kigali from Brussels after the massacres, it was "like a horror movie", silent and completely empty except for the crows and the shamefaced dogs that had gorged on the bodies.

It's my first night at Xaranna, a safari lodge on an island in the Okavango delta. We eat outdoors at a long table, as the shape of a hippo ploughs the moonlit water and tiny reed frogs make their xylophone music.

On a mysterious wooded island on Lake Como, reachable only by boat, there is a restaurant where the same set menu has been served since 1947. It is perfect, so why change it? And at the end of the meal - of every meal served there - the proprietor performs an exorcism to rid the island of a curse dating back to the 12th century.

The weekly goat auction in Nizwa, the former capital of Oman, is a mixture of Crufts gone wild and a Wall Street trading floor, and everyone is far too busy to give me, a western woman, even a glance.

Some men hold staffs, dead ringers for Abraham, their brown faces deeply furrowed as they watch the display of struggling goats and cows. It's like stumbling into the Old Testament.

Forget scenic helicopter rides or private jets. This is the way to fly - like a bird, like an angel, swooping through the sky above the Zambezi with nothing between the ground and my dangling feet but air. Icarus didn't have the advantage of technology, but his father had the right idea. Today, I have wings.

I went to the Golden Door hoping for glitz. Well, it's the place that spearheaded the spa revolution when it opened in 1958, and it remains the byword for beauty in La-La Land. I imagined excessive vulgarity. I imagined breast-enhanced, blonde Hollywood types. I imagined Courtney Love would be there, and at least one Hollywood star would be trying unsuccessfully to overcome their drug or drink addiction. After all, it's the former hang-out of Zsa Zsa Gabor, and she was hardly understated. Nicole Kidman's been here. And Alicia Silverstone, Olivia Newton-John, Oprah Winfrey, Barbra Streisand. The exercise rooms would be marble, at least. The facials maybe using caviar. It would surely be super-glamorous.

If I had to survive in the bush, I'd kill a buffalo," announces my son, Michael, aged 19.

"How?"

"I'd get a huge stone and crash it on his head."

The young Masai warrior who is with us begins to laugh, long and deep. This is clearly the funniest thing he's heard in a while. It's like a Masai telling us he would survive in London by asking a passer-by for £100.

Los Angeles is a land where conventional time no longer exists. "There are no seasons, it's always the same sunny blue sky day after day, so you never feel you're getting any older," said a friend, tranquilly. Here you can pause the passing of the years, or even rewind a little - breasts can be pert again, skin taut, forehead uncreased.

Pearly light shimmers off the early-morning ocean as a swimmer breaks the water, tearing a surface as still, tense and silver as mercury. Back on shore, life has a less subtle, more primary palette: a breakfast of orange guavas and fresh cherry juice watched by an inquisitive yellow-eyed blackbird and a tiny bananaquit, hovering over white and pink hibiscus.

In the vibrant restaurants and bars, the energy and attitude are palpable. And if you want to understand America and its present policies, you need to see its dreams made stone in the great monuments of Washington.

Now, Dyke is a safari guide. The skills he learnt as a child have been developed to a fine pitch of awareness: nothing escapes him, no sound or sight or movement. If you want to understand African wildlife, it’s worth knowing Dyke, or someone very like him. Without a good guide, the bush will be just bush, with a few impala jumping around and an odd sighting of a giraffe’s head. It is the guide whose determination and skills take you within a few feet of animals so beautiful, your life shifts on its axis.

They were the colour of the sun. Or, rather, the colours: dancing in the steamy heat next to a deserted waterfall, they seemed to have soaked up its every tone and mood — the pale lemon of morning, the fierce yellow-white of midday, the livid burnt orange of sunset, all picked out against the green vegetation. Like little pairs of magically animated flower petals, they flirted and flitted in an intricate ballet. It’s worth coming to the Dominican Republic just for the butterflies.

The effect of the clean air of South Africa, and the heat and the light and the sumptuous landscape, was instant. Gone was the cough, back was the energy, and there was virtually no jet lag; it was as though I’d somehow wandered through the back of the wardrobe and found the antithesis of London waiting for me there. The dirty grey bowl that hangs over our capital in winter was replaced by a dome of blue sky during the day and stars at night. What is more, everyone speaks English and drives on the left- hand side of the road. It’s a glorious alternative reality.

In Jamaica, even dominoes is a drama. “It’s a man’s game, dominoes,” a cab driver tells me. “They’re so loud, man, you can hear them slappin’ the table a mile away”. The weather is equally theatrical, with the raw sun tempered by sudden rainstorms and the sky putting on a pageant every morning and every night.

In the still humid evening, little kids (only ever one with each couple) are led by doting parents. Everything is different here — the chef in white uniform sitting on a step in the shadows, eating a white ice lolly, the restaurant where a pampered child is choosing a fish to eat as if choosing a pet, the sex shop with the careful Chinese writing that makes it look charmingly decorative rather than seedy. Then there are sellers of meat, makers of food, everything piled high, everything out in the street.

One of my companions in flip-flops began to move restlessly from side to side, no longer so enamoured of the landscape of Indian Canyons. The canyons lie to the south of Palm Springs, a place more famous for its celebrity mansions and golf courses than its natural wonders. But it is the wonders that first lured celebrities and golf out into the desert. Two hours from Los Angeles and encircled by mountains, the region is still part-owned by the Cahuilla Indians, and has dry desert air that keeps people alive well after their time.

Taking a tango lesson at the dancers’ flat wasn’t, perhaps, the behaviour of a cautious person, but Buenos Aires invites a spirit of adventure. It is a city on the edge. The wide, confident avenues explode with blossom, but if you look closer, the pavements are disintegrating. The central Obelisco on the Plaza de la Republica thrusts up into the sky, a symbol of Argentinian machismo, but on the grass beneath it, a group of police officers stand over a spread-eagled man. He is face down and handcuffed; and one policeman has his foot on the man’s back.

If you fear Hawaii will trap you in a picture-postcard of palm trees, think again. You can certainly have palm trees, perfect beaches, dramatic surfing, sensual hula dancing, even more sensual massages, delicate Asian food, beautiful waterfalls and continuous divine weather; but the real reason to come all this way is, in some curious way, to make you touch base.