It is over 50 years ago but the first film I remember seeing was The Magnificent Seven, in the old Playhouse cinema in North Berwick, and I always fancied doing what Yul Brynner and Steve McQueen did, crossing the Rio Grande and riding into some sleepy little Mexican town. It took me half a century, but I did it.

I walked down to the river from the US border post, which opens five days a week, and the ferryman rowed me across the Rio Grande. I hired a donkey and, with Elmer Bernstein’s iconic soundtrack playing in my head, I rode into Boquillas del Carmen, the sort of village where customers arrive at the saloon on horseback.

Later, in a packed bar that used to be a theatre, in the old Texan mining ghost-town of Terlingua, where I was camping, I regaled fellow drinkers with my tale. The regulars used to include a goat. He was once elected mayor, but he died, so now he is stuffed and stands beside the stage, with a bottle of beer in his mouth. But anyway I met a guy who bought me a pint and laid down another challenge…

Back story: I am 58, mortgage paid, children through university. I have been a lot of places, but there were many more I wanted to visit. So I decided to go right round the world, on a budget, with a backpack. I would cross two continents by train, I would see dragons and cradle a mermaid in my arms, I would run round Uluru (Ayers Rock) in temperatures that I was told would kill me and I would reach the summit of the tallest mountain in the world – no, not Everest, cue QI klaxon.

The trip took just over three months and my route was Edinburgh, Istanbul, Kuala Lumpur, Borneo, Bali, Komodo, Darwin to Adelaide by train, Melbourne, Sydney, New Zealand, Tahiti, Hawaii, across the US by train, Chicago, Iceland, Glasgow and along the M8 to Edinburgh. There were planes (22 in all), trains and automobiles, boats of every shape and size, one bicycle and one donkey.

In the end there were so many amazing places and experiences (and people) that it was difficult to pick highlights, but if forced to pick a Top Ten it would look something like this ...

10 New Orleans

New Orleans pips Chicago, for its culture, including voodoo and jazz; for the mighty Mississippi River, which you can cross by ferry for $2; and for the food. I did a culinary tour and twice visited Antoine’s. I think some of the waiters have been there since it opened before the Civil War. Most days it serves a three-course lunch for $20.16, (around £15) including oysters and alligator bisque, with a cocktail of the day for 25 cents, though there is a limit of three. Sadly, on my first visit the cocktail was Bloody Mary and I hate tomato juice, so could manage only two.

9 Tongariro Alpine Crossing, New Zealand

My wife Jenny joined me in New Zealand for a fortnight and the most spectacular scenery we saw was on a 13-mile trek across the otherworldly, ever-changing, volcanic landscape of Tongariro National Park, with steam seeping from the ground and lakes of various colours, like someone had tipped paint into them.

8 Coast to coast across Australia by train, Darwin to Adelaide

Named after the Afghan camel drivers that established the route, The Ghan train is over a third of a mile long. There is a certain fascination as it rolls across flat, dry, empty landscape. I split the two-day journey by stopping in Alice Springs and going to Uluru. A £250 pass was the cheapest option and would have covered the east-west service too, if I had had time.

7 Coast to coast across America by train, LA to New Orleans

Amtrak was better value at £120 for another two-day journey. I began in LA at 10pm, my third successive night without a bed, following overnight plane and bus journeys. The train ran along the Mexican border, the rugged landscape of Hollywood westerns. I got off in the town of Alpine. The baggage compartment is not opened here, so alighting passengers are restricted to carry-on luggage, which determined the size of my backpack for my whole trip.

6 Borneo

One of the principal reasons for my trip was to see orang-utans in the wild, which I did on the Kinabatangan River. My fallback was Sepilok rehabilitation centre, where one big, mature adult and a slightly younger ape came striding towards me on the boardwalk. What is the etiquette there then? Another visitor got a couple of shots of me pressing myself against the handrail, creating as wide a berth as possible.

5 Hawaii (Big Island)

Hawaii had awesome waterfalls and volcanic craters. And it was here that I did my most expensive day trip (£120), to the top of Mauna Kea, which is the tallest mountain in the world when measuring from its base beneath the ocean. Our guide advised on how long we should spend at the visitor centre, half way up, getting used to the thin air. He stopped telling people exactly how much less oxygen there was at the top after an entire car-load decided they could not breath and insisted on turning back. But the biggest thrill on Hawaii was the Big Island Half-Marathon. It was hilly, it rained and temperatures were way below usual. It suited me perfectly, though I was amazed to win my age division. This is the first time in my life that I have actually mounted a podium and I milked it for all it was worth.

4 Uluru (Ayers Rock)

My intention was to drive from Alice, 280 miles away, but ultimately I joined a group, sleeping in the Outback dirt and all mucking in at camp, some more than others. It was like being on I’m a Celebrity or Two Tribes, as the group fractured from the start. I thought we were going to arrive at Uluru at dawn, but we got there early afternoon, with temperatures in the high 30s. I had hoped to run round it. Andy, the guide, said unambiguously: “You would die”, only to change tack after further discussion. I managed it and ran 10 miles without mishap, though one of the group had to go to hospital with dehydration from trying to walk round. I spent three days trekking in the Red Centre, one of the most dramatic landscapes I have ever seen, pretty much how I imagine Mars should look. Andy did not help heal the rifts in the party when he suggested on the last night that our wee tribe sit down and drink our carry-out while everyone else did the chores, because we had done so much work everywhere else.

3 Big Bend National Park, West Texas

As I drove 100 miles south from Alpine, the radio stations faded into the mountains until there was only one left, a church-sponsored country and western station. Every song seemed to be about someone who led a wild life and then discovered God. Eventually even God gave up on me and all I had was static. On the first day in Big Bend I did The Magnificent Seven (the real one, not the remake) border crossing. That night the Starlight Theatre bar at Terlingua was full of a wonderful mix of campers and the locals who had begun to repopulate the ghost town. I am not sure how representative they were of Texas, given that Terlingua is described as “a community of artists, musicians and other free-thinkers”. Next day I determined to fulfil the promise I made in the bar the night before… So I swam to Mexico. Of course I checked it out on Google first… and discovered more people fall victim to the currents and hidden dangers of the river, than fall victim to flash floods, snakes and drug smugglers. On my third day I did a full-day trek through the park. Beyond warnings of bears and mountain lions and beneath the circling vultures were hills that rolled on forever without sign of human habitation. Later I met a guy who had been sitting at the viewpoint and he felt so inspired that he proposed to his girlfriend. He maintained it was completely spontaneous. Good luck with that then.

2 Komodo

As well as orang-utans, I especially wanted to see Komodo dragons, lizards that grow to eight feet and whose bite can be lethal, as seen in the James Bond film Skyfall. Three of us hired a boat for an overnight trip to the island, with a crew of three. It cost us £50 each. And while our guide, armed with an old-tech stick, urged us to get closer to the prehistoric giants for photos, another guide was telling his group to stay back. Next day I woke on the boat to the sight of flying foxes (the world’s biggest bats, with a five-foot wingspan) returning to their roosts. But the highlight was an orphaned dugong or sea cow on the island of Kanawa. These strange, docile vegetarians may have been the inspiration for mermaids. It was a baby, about the size of a seal, and the islanders were bottle-feeding it. Our group included one woman and when she swam on her back it was clearly trying to suckle her. I do not know what it was doing in my midriff, but it was tickly. Sunset at Labuan Bajo, our starting point, seemed to feature every possible type of cloud, with red, orange and blues splashed across the sky like a Van Gogh painting.

1 Bora Bora

It is easy to see why Gaugin was so inspired by the Tahitian islands, with blue lagoons and mountains rising sheer from the sea, covered in dense, green jungle. And Bora Bora is special from the moment you see it from the plane. The airport is on its own little island or motu, and you get a boat to the main island or to a private motu, with cabins built on stilts over the water. I spent a lazy day on one such island, dividing my time between beach, pool and bar. As the shadows lengthened, back on the main island, I went in search of one of the cannons I had heard the Americans left behind after the Second World War. On a steep hillside there it was, like a sinister index finger pointing across the glistening waters at the oblivious tourists on Motu Tevairaoa. The combination of rusting, forgotten artillery, idyllic seaside panorama and the solitude seemed eerie, poignant and strangely familiar, like I had been there before. Bora Bora was also the scene of my most memorable snorkelling trip ever. Beneath those sun-kissed waters, glide majestic manta rays, like a giant, alien life form, and lemon sharks that I reckoned were about six feet until someone dived down, and either I misjudged or the guy was only three feet tall. I actually stood on a stingray, but it was in deep water, so it did not feel my full weight. And while a sting might have been painful, it would not have been deadly – Steve Irwin was desperately unlucky that a stingray’s barb pierced his heart. Later I sit and gaze at Bora Bora’s two mountains, side by side. One is shaped like a manta ray’s head, with two peaks. The other is flat on top. It is only slightly higher, but it always seemed to be veiled in cloud. Watching clouds drift slowly across the sky and light dancing on the mountains, anyone might feel they could become an artist.

TRAVEL NOTES

Airline alliances offer round-the-world tickets, but the only way I could string together the places I wanted to go was with individual flights. I used a specialist agency BootsnAll and its excellent website to build my basic itinerary and booked short-haul flights direct while travelling. I booked trains in advance with Amtrak in the US and Great Southern Rail in Australia.

I stayed in Airbnb, where possible. Staying with local people had obvious advantages. In Chicago I even managed to borrow a fleece when the temperature was 2 degrees and most of my clothes were soaking wet. I also used Booking.com and slept in hotels, hostels, a tent and on the ground. Sometimes I booked weeks in advance, sometimes just a few days.

I was aiming at an overall cost of £10,000, with half going on travel, and a daily spend of around £25 on accommodation and £25 for everything else, which proved a little unrealistic. Prices varied widely – Asia was cheap, Tahiti expensive, Iceland extortionate. My final cost was around £11,500.