Spread like toy building blocks across the steep-sided mesas at the foot of New Mexico's Jemez Mountains, the town is on land that was originally settled by the Pueblo people, whose culture remains etched into the surrounding pink and red rock.

It was transformed in 1943 when the sleepy community of ranchers, entrepreneurs and merchants was chosen as headquarters for the Manhattan Project, the codename for the development of the first atomic bomb.

As the project leader, physicist J. Robert Oppenheimer, explained, it was remote, secure and sparsely populated but still big and beautiful enough to "keep a bunch of prima donnas happy" working year-round in the state's outdoors.

After centuries of anonymity, Los Alamos (Spanish for cottonwoods) became "the town that never was", so hush-hush that its residents had no official identity and no direct mailing address. And for years after the war – effectively ended by the Los Alamos bombs dropped on Hiroshima and Nagasaki – it continued to exist only "in a sort of official government limbo", local historian Marjorie Bell Chambers explains.

Today, the self-styled "birthplace of the atomic age" and the "place where discoveries happen" is, well, booming.

The city is home to the Los Alamos National Laboratory, which employs more than 11,000 people specialising in hush-hush, high-tech security. And it now has another industry – tourists. From all over the world they come, to be variously appalled, attracted and intrigued by a killing device so scary it prompted "Oppy" to quote the Hindu Bhagavad Gita: "I am become Death, the destroyer of worlds."

The Lonely Planet's investigator, at least in my guidebook, was "disturbed to find only the tiniest mention of the destruction of the two Japanese cities" with some 200,000 deaths. But visitors prepared to trawl through the museums will find social, scientific and political issues addressed.

Still, Los Alamos remains an odd place. Not far from the laboratory is the Omega Peace Institute and the First Church of High Technology, which celebrates critical mass every Sunday. Pro-nuclear badges compete with jokey car bumper stickers reading "Nuke a gay whale for Jesus".

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But then, most of New Mexico is odd. Wonderfully, eccentrically, eclectically odd. A place of icons: Route 66, the "mother road"; the mighty Rio Grande; and the Santa Fe railroad. It is a Land of Enchantment, as the official state slogan proudly proclaims.

It's also a state that within a day's drive – though it demands several weeks – offers everything from the truly banal to the beautiful, from prehistoric villages to space-age installations and from sublime desert art (Santa Fe) to snake-oil magic (Albuquerque) and, of course, UFO lunacy (Roswell).

The eerie sense of other-worldliness begins when the visitor lands in Albuquerque, a mile-high city (about 1600 metres) of some half a million souls, sprawled across flat desert and surrounded by mountains tall enough to tire first-timers.

One-third Spanish-speaking, Albuquerque is high, dry and only intermittently handsome. Downtown could be Anywhereville, USA. The Rio Grande hereabouts is more murky than mighty. And though its flyovers are sympathetically painted ochre and azure – the colours of pueblo mud and high, wide skies – Route 66 can actually be a real drag.

But there are better places to get your kicks and other things to see and do. Take a trip by tram or car up the "melon-shaped mountains" to Sandia Peak or across the city by balloon for top views. View the Pueblo rock art by hiking through the Petroglyph National Monument park. Spend a few hours exploring the life, history and culture of the area at Albuquerque's opulent Museum of Art and History and Indian Pueblo Cultural Centre, where native women wriggle and giggle as they do the pot – as in colourful pottery – dance.

Or head with the tourist herd to the Old Town for a plate of enchiladas at a cheerful restaurant such as Casa de Fiesta, take a look at the historic Church of San Felipe de Neri and a tour of the self-styled International Rattlesnake Museum.

It sounds cheesy and some of it is. Director Bob Myers, a former high school biology teacher, aims to provide you with all you want to know and more about the rattler's place in American history and culture.

Thus, there are advertisements for products such as the Grand Canyon Rattlesnake beer, demonstrations of Indian snake dances, a section on "rattlers in the movies" and cartoons of the Gary Larson variety. One such cartoon features a straying rattler returning to her lover. "I'll come back for you, Sidney," she hisses, "but I won't crawl." The live displays featuring horny toads, spiders, scorpions, hissing cockroaches and hundreds of different species of snake are quite compelling, especially in the small shop setting that prevents Myers showing more than a tenth of his amazing collection.

And yes, Myers has been bitten by a rattler – not in the wild but in his backyard while "preparing" one for a photo shoot. So was it painful? "Put it this way, I wouldn't recommend it to any of my friends," he says.

Albuquerque offers more than enough of the "great indoors" for afternoons when visitors are sent scurrying inside by rain and bitter, cold winds. Nor is such harsh weather totally unwelcome. By the next morning, it has transformed the hills and mountains around the city into a winter wonderland of dazzling, blue skies and pristine white snow, piled up against a rocky landscape painted many shades of pink and red.

They make the perfect backdrop for a scenic drive through the Jemez Mountains, past several hospitable Pueblo settlements and into the back country of the volcanic Valles Caldera National Preserve and the Bandelier National Monument.

Named after a Swiss-American archaeologist, Grand Canyon-like Bandelier was the site of Pueblo Indian settlements for more than four centuries until the late 1500s when it is believed civil unrest and worsening drought caused them to be abandoned.

So spectacular are the views, so prolific the wildlife, so thrilling the exploration of ruined underground chambers, or kivas, and cliff-side caves – reached by rope ladders running tens of metres above the volcano floor – that a whole day can be spent hiking through Frijoles Canyon at Bandelier. At least don't try to tag it on to a day's trip to nearby Santa Fe.

The New Mexico state capital is old, arty, elegant, easy going and one of the top domestic destinations for American tourists. Deservedly so.

Though it can be clogged with tourist traffic queuing for places in 21st century, pueblo-style parking stations, its principal attractions can be easily walked. At "the heart and soul" of the city is Santa Fe Plaza, ideal for snacking, bartering and people-watching.

Along one side is the Palace of Governors. Outside, native Americans sell all sorts of colourful handicrafts. Inside, maps, pictures and displays illustrate half a millennium of New Mexican history, from Spanish conquest through to frontier times of the Santa Fe trail to the present day.

Just off the square is your pick of the 400 or so art galleries in Santa Fe and the Georgia O'Keeffe Museum, dedicated to the work of one of America's leading modern artists and some of her equally impressive contemporaries.

O'Keeffe, who was born in Wisconsin, fell in love with "vast, empty and untouchable" New Mexico on her first visit in 1929.

"I'd never seen anything like it before but it fitted me exactly," she explained. "It's something that's in the air. It's different." She later moved here permanently, endlessly painting its flowers, its deserts, its shapes and its moods and capturing its amazing colours.

For a contrast, only a few blocks away is the Chuck Jones gallery, an exuberant, visitor-friendly place that showcases the cartoons of another one-time resident who brought to life Daffy Duck, Road Runner, Wile E Coyote and Bugs Bunny.

The French-designed cathedral of St Francis is just off the plaza, as is the popular Loretto Chapel. It features a remarkable – some say, miraculous – 360-degree spiral staircase, which seems to twist in the air without central or other visible means of support. Legend has it that it is the work of an unknown carpenter who arrived on a donkey, erected the staircase using only a hammer and saw and rode off before the astounded nuns could pay him.

No visit to Santa Fe would be complete without a visit to the local railway depot, not so much to see old trains but to admire their modern successor, the red, yellow and silver Rail Runner Express. Above all, perhaps, Santa Fe is a great place to hang out and breathe in the wonderful sights, sounds and smells of one of America's oldest and most memorable cities.

Time permitting, travellers to New Mexico should also take in Taos and Roswell. Two more different places, at opposite ends of the state, it is difficult to imagine.

Taos has been described as the state's favourite arts town, "wedged between the towering peaks of the Rocky Mountains and the plunging chasm of the Rio Grande gorge" – part hippie, part Pueblo, part creeping commercialism of the sort that has covered the state with casinos.

It has odd museums, great eateries, skiing, hiking and fishing and a ranch-side memorial to English writer D.H. Lawrence, who lived here briefly in the 1920s. His wife, Frieda, returned and died here many years later. It is believed Lawrence's ashes were also taken to the Taos ranch where they were mixed with cement used in building.

And, so, finally to Roswell, a centre of farms, factories and oil wells whose reputation as a tourist destination is based on an event that almost certainly never happened. If it did, it was at a site almost 100 kilometres out of town: the crash-landing of an alien spacecraft.

The so-called Roswell UFO Incident happened on July 7, 1947. The United States military has always maintained the resulting debris was that of an experimental high altitude surveillance balloon. UFO enthusiasts insist this was a cover-up and bodies were recovered from the crashed alien craft. Whatever. The whole story may be explored at the UFO Museum and Research Centre on North Main.

The craft is currently housed in a movie house but there are plans to build a futuristic new facility opposite the only UFO-themed McDonald's restaurant in the world.

Each July, the Great Roswell UFO Festival draws "the curious, the silly and the serious" to the community in search of what's "out there". Quite what is out there remains uncertain but as O'Keeffe once said, there's certainly something in the air of New Mexico.

FAST FACTS

Staying and eating there

Albuquerque is the best base for day trips north to Santa Fe and beyond, or south to the dubious charms of Roswell. Accommodation is abundant and reasonably priced, from about NZ$300 for luxury hotels such as Hyatt Regency to NZ$70 for the good value Suburban Extended Stay.

Things to do

See newmexico.org for an overview. Then collect handfuls of state-wide maps and brochures from the visitor centre in Old Town Albuquerque (itsatrip.org). Nowhere does tourism better but check opening hours of galleries and museums (some close Monday or Tuesday depending on season). Check mountain tram times at sandiapeak.com.