For the fifth largest state in the Union, Arizona is spookily under-populated. Only five million people live in its 113,000 square miles, and most of them in the cities of Phoenix, Tucson and Flagstaff. The essence of the state, as the traveller soon discovers, is its mountain ranges, canyons, mesas, buttes and spires – terracotta-reddish, lunar plains of wind-scoured, water-eroded, volcano-blitzed rock. No wonder the Native Americans worshipped the land spirits; no wonder 19th-century European settlers mythologised cowboy life and invented the drama of the Noble Horseman, framed against the wildest landscapes they'd ever seen. No wonder that writers, searching for a made-up name for a no-horse town, came up with "Nowheresville, Arizona".
Today, you can shop for hours in Scottsdale – the Bluewater of Phoenix – and find charming hotels and classy restaurants under the Camelback Mountain or amid the chakras and vortexes of Sedona, America's spiritual capital. But luxury, comfort and retail therapy aren't the point of visiting Arizona. The point is to be on the move, by car or on horseback, gazing at the unrolling vistas of astounding scenery, at scrubby desert and waving sagebrush, Colorado plateau and Navajo reservation, as you gradually realise the entire state is on a kind of ramp.
Down south on the flat plains around Tucson, near the Mexican border, you're barely above sea level, and the heat is intense. North of Phoenix, heading for the Martian extravagance of the Grand Canyon, you find yourself getting out of breath (and considerably chillier) 7,000 or 8,000 feet above sea level. There are mountains and desert in both regions, but visitors with sedentary lifestyles will have a less breathless time down south.
You can try refusing to join in the cowboy schtick, but it'll get you in the end: you'll acquire the boots, the hat, the shirt and possibly the horse too – dude ranches are popular, taking in beginners and seasoned equestrians alike. You'll find mock-ups of Western bars everywhere, hammy shoot-outs in the street in Tombstone (home of the OK Corral), studio back-lots where they once filmed classic Westerns – and ancient bunkhouses, where they serve green-chilli burgers with tequila shots and Don Camino beers, and a grizzled guitarist will play Lynyrd Skynyrd's "Freebird" in the style of Seasick Steve, while couples dance a two-step under a chandelier hanging from a tamarisk tree.
Tucson, the second city, and the heart of the southern desert regions, is charmingly small-scale and manageable, a good-natured town that basks in a 500-square-mile valley surrounded by five mountain ranges. Its few skyscrapers seem rather an irrelevance. Visitors will head instead for the gleaming white cathedral, the groovy shopping precinct of Sixth Avenue, the old "Barrio" business district, the El Presidio Historic District, and the brilliantly garish Congress Hotel, where John ("Public Enemy No 1") Dillinger was nailed by the G-Men in 1934.
And then it'll be time to get back into your Mustang convertible and hit Interstate 10 again, hurtling into the ancient desert with the Santa Catalina mountains ahead of you and Saguaro National Park, with its 200-year-old cactuses, on either side; or you'll take the popular 120-mile round trip of the Apache Trail, to gaze at the Superstitious Mountains and the Roosevelt Dam along the way. You could resign yourself to just driving all day through this wonderful territory of golden deserts and sudden pine forests, noting the ridiculous place-names – Bumble Bee, Horsethief Basin, Badger Springs, Dead Horse Ranch – and looking forward to your next chilli burger and beer.
Or you could think, "Sod all this tourism", embrace your outlaw spirit, unleash the bad-ass in your soul and light out west on the I-8 freeway heading for Yuma on the extreme western border, the home of the famous cowboy prison, where you can meet the legendary 3.10 train, full of hardened criminals like yourself ...
* Follow in the footsteps of Moses on his route into Egypt's wilderness on a desert trek that takes in Mt Sinai and the rock where he made water flow. Overnight under the stars in the Blue Desert. Seven days from £475 not incl. flights (20 per cent invested in local projects). Bedouinpaths.com
* Set in the lunar landscape of Chile's Atacama Desert, Explora is a wilderness lodge surrounded by snow-capped volcanoes, salt flats and pre-Inca ruins. Inside, Andean tapestries contrast with hi-tech telescopes; visibility here for star-gazing is unparalleled. 00 56 23 952533; explora.com
* Namibia's Little Kulala Lodge is the only man-made feature amid 21,000 hectares of red sand dunes in the Namib Desert. Thatched canvas chalets have wrap-around verandas and viewing platforms, but for superlative vistas take a dawn hot-air balloon ride. Namibweb.com/lkulala.htm
* There is no desert quite like Oman's Empty Quarter. Follow in the footsteps of Thesiger with Pioneer Expeditions' new "full moon desert trek", guided by Bedu tribesmen, and learn how to tend camels, seek out desert foxes and use the stars as guides. 0845 0047 801; pioneerexpeditions.com