“FIRST time in Vegas ma’am?” the taxi driver deduced from my dazed expression. Despite having seen this neon wonderland in countless movies and television shows, I still wasn’t quite prepared for ‘the strip’ in the flesh, especially after a 12-hour flight.

Little did I know, however, that over the next week I’d see sights more surreal and incredible than anything Vegas could throw at me – and all of them completely natural.

My Grand American Adventure would begin and end in Sin City, taking in Route 66 and the mighty Grand Canyon; but before that, I’d be hiking my way through two other national parks and traversing one of the most wild and dangerous valleys in the world – well, if you believe the John Wayne version.

After meeting the rest of the tour group – 12 intrepid travellers aged from 28 to 80-something, we boarded our bus and set off for Zion National Park. Early Mormon settlers considered the canyon their promised land, and as a result most of its towering sandstone cliffs bear names with a religious link: the Three Patriarchs, Cathedral Mountain and the Altar of Sacrifice are all reminders of Zion’s early beginnings.

One of the park’s most famous peaks is Angel’s Landing, and the climb to the top – 1,500ft above the valley floor, is also one of its most popular.

Following the advice of our guide Jeff, we were on the trail by 8.30am to avoid walking in the searing midday sun, but even that couldn’t help me on the last leg of the journey. One look at the people in front scrambling up and down an almost vertical cliff face with nothing more than a single chain rope to guide them and I wimped out, opting instead to walk the West Rim route to a sun-soaked plateau and the perfect picnic spot.

There are walks for all abilities, with the easiest also proving among the prettiest. The 5km Pa’rus Trail traces the Virgin River as it carves its way through the canyon, and captures the tranquillity and integrity of the park perfectly.

The next morning we left Zion, climbing the Colorado Plateau in our coach to Bryce Canyon National Park – and one of the most remarkable landscapes on earth.

Bryce is famed for its hoodoos – surreal rock spires in a kaleidoscope of colours that create forests made of stone, like something out of a George Lucas fantasy.

Technically Bryce isn’t a canyon at all, as most of the sculpting is done by a constant cycle of freezing and thawing, rather than by a river. Its elevation means that for around 200 days a year, ice and snow cover the park, melting during the day and refreezing at night, eroding the rocks from the inside and creating the hoodoos.

The walk around the rim gave plenty of photo opportunities, but getting in among the spires is the best way to appreciate the true scale, and fragility, of this bizarre landscape. Starting off at Sunrise Point, we walked down into the canyon while enjoying a game of hoodoo bingo – trying to match the distinctively shaped rocks to those named in our park guide, with varying degrees of success.

Each of the National Parks on our tour produces a free newspaper full of essential info, great maps – and some terrifying statistics. There are mountain lions and black bears at Bryce, although your chances of seeing them are slim; no, here you’re much more likely to be killed, or seriously injured, by falling off a cliff or being hit by lightning.

Rockfall is another threat. The walk up the winding switchbacks of Wall Street, one of Bryce Canyon’s most spectacular hikes, is a must for any fairly fit visitor. But don't linger too long, crumbling cliffs are common and the route is regularly closed off because of rocks falling from above.

As well as its hoodoos, Bryce is famed for its dark night sky. So one night we convinced Jeff to drive us back into the park to see nature’s great light show.

Experts say that even without a telescope you can see up to 7,500 stars here.

Back on the road we made a brief stop to admire Lake Powell and Glen Canyon, before arriving at Monument Valley, Arizona, home to the Navajo people and the location of countless Western movies. Looking out across the dusty valley, the huge red monoliths of The Mittens and Merrick Butte staring defiantly back, I could almost hear the The Big Country theme tune playing in the background.

Local guides offer jeep tours, providing a fascinating insight into Native American culture and the valley’s colourful history.

It was time to get our first glimpse of the Grand Canyon. At 277 miles long, 18 miles wide and more than a mile deep, it really is impossible to comprehend the true scale of this wonder of the world.

I stood mesmerised as the changing light brought the canyon to life. With every passing cloud it seemed to shift, its multicoloured layers deepening to bold reds and greens, or fading to a gentle painted haze. It’s a truly humbling sight.

Grand Canyon Village is busy with day trippers but it’s worth enduring the crowds to check out historic buildings such as the Kolb Studio and Hopi House. And an escape from it all is just a short walk away on the Hermit Road route.

The view from Hopi Point is a particular highlight, a breathtaking 90-mile east-west panorama of the canyon.

Heading west, we watched the Colorado River slice through the canyon, as six Californian Condors circled serenely overhead. This is one of few places on earth you can still see this rare bird in the wild.

The next morning, a helicopter ride over the canyon gave me my very own bird’s-eye view, and even though I’d looked at little else for the previous 24 hours, the sight of the canyon as the chopper dropped off the edge of Kaibab National Forest down into the valley literally took my breath away. It’s incomparable. A two-billion-year-old masterpiece.

Back in Las Vegas, I swapped the hiking boots for my heels and hit the strip. I grinned like a kid at Christmas as the Bellagio’s dancing fountains performed to Elvis’s Viva Las Vegas, and was able to visit the Pyramids, Paris, Venice, New York, all in a single evening.

But despite the glitz and glamour, it’s the dignified walls of Zion glowing red in the late afternoon sun, of Bryce’s other-worldly spires; of Monument Valley's proud monoliths, and the awesome, ever-changing Grand Canyon that remains in the foremost of my mind.

Next to them, the bright lights of Vegas pale in comparison.

Travel facts

Claire Walker joined the Canyons and Indian Lands tour by Grand American Adventures, which offers a six-night package from £1,549 including return flights ex-Heathrow into Las Vegas, room-only hotel accommodation, in-country transportation, professional tour leader, entrance to Grand Canyon IMAX theatre, guided walks and hikes through Monument Valley, Bryce Canyon and Zion National Park, plus sunrise or sunset tour of Grand Canyon.

For reservations, call 0844 576 1406 or visit grandamericanadventures.com