The image of Texas widely held might not encourage the timorous traveller to head that-aways. Texas is usually viewed as a flat desolation roughly the size of France and Spain combined, full of hard-bitten rednecks at best and out-and-out psychopaths at worst, such as have been portrayed in films such as Bonnie and Clyde and, more recently, No Country for Old Men. The reality is somewhat at variance with the image. West Texas is attractive rolling hill country, and far West Texas, that portion beyond the River Pecos, is mostly mountainous, rising to almost 9,000ft in Texas' highest point, Guadeloupe Peak. This is a wild and empty country, the location of some of the most rugged and remote corners of the US outside Alaska, and home to two staggering National Parks that get very few visitors due to their location. West Texans are also the friendliest folk I have met in my travels in the US. When they say, "Howdy, y'awl, how ya doin'?" they mean it.

That was not my first impression on landing at El Paso airport, and being quizzed by the immigration officer as to my reasons for coming to El Paso. "Nobody comes to El Paso on vacation," I was told. The Rio Grande separates El Paso from Mexico and the problems of people and drug smuggling are notorious. I managed to mollify my interrogator by stating that my destination was actually Big Bend National Park – 350 miles south. El Paso is the place to start any trip to West Texas and, amid desert and mountains with an almost 100 per cent Hispanic population, you immediately realise you are in the the land of canyons and cowboys. El Paso is nearer the Pacific Ocean than it is the Gulf of Mexico. Winter is almost unknown here, and down at Big Bend they get snow on the highest mountains for a couple of days at most. January midday temperatures are around 15-20C.

Despite the fact nobody comes to El Paso on vacation, take a look around before heading off. Lodgings are cheap but unless you want to stay in one of the endless anodyne American chain motels the place to go is the Camino Real hotel, designed by local architect Henry C Trost. This is an astonishing palace of tiffany glass, marble pillars and utter luxury where a jazz band plays in the vaulted bar of an evening. It was built in the cattle and railroad glory days of El Paso and has more than 200 rooms. When I was there half a dozen were occupied and, since El Paso is boomtown no more, my night cost me about $75. It lies in the dead centre of the city, and dead means dead, El Paso being an extreme example of what has happened with many US cities. Block after block of fine buildings stand utterly empty round the hotel, many of them designed by Trost, who married Art Deco with Hispanic style. A street away starts the Hispanic barrio, where I was the only white person among thousands of Hispanics. It was not threatening, but it was sad; the housing conditions here are what you would never see in any European city, as is the poverty and the pollution. Mexico is reclaiming the south-west, stolen by Texas and the US back in the 1840s, when El Paso was Mexico.

From El Paso it is a long way to Big Bend, but on empty roads that are a pleasure to drive. The various counties of far West Texas are among the least densely populated areas of the entire United States. These are places where you don't want to run out of petrol – or water. You can drive 100 miles without seeing a car, never mind a house. There are not many towns on the way, and first of note is Marfa where the 1956 epic Giant was shot and near where one of its stars James Dean was killed in a car crash shortly after finishing shooting, and where another Trost luxury establishment, the Hotel Paisano, housed the cast including Liz Taylor and Rock Hudson for the duration of the filming. You can stay there at rock-bottom winter rates and imagine yourself a film star. Then from Alpine, around which the Coen brothers' No Country for Old Men is set, you branch off down a back road towards Big Bend which seems to be the end of the world, with the huge cliffs on the south side of the Rio Grande at St Elena canyon, blocking out Mexico. Theoretically the border is closed here, but you can wade the Rio Grande easily, and many Mexicans do so, coming over to sell items to the tourists around the hot springs at Rio Grande Village.

There is a lodge up in the park at Big Bend where you can stay, but the fun place to stay is the town of Terlingua, which lies just outside the park, and which, if you have seen Wim Wenders’ masterpiece Paris, Texas, features in the first part of the film. It is instantly recognisable from features of the desert landscape such as the dramatic Mule Ears, whence Harry Dean Stanton's Travis emerges to Ry Cooder’s haunting soundtrack. Terlingua is one of the few places in the USA where a genuine counter-cultural ambience still survives. There are people here living in abandoned miners shacks and singing for their supper in the Starlight Theatre, an old cinema from the time when Terlingua was a mercury mining town, the mines largely worked by Mexican labourers, whose old Catholic church and graveyard form a forlorn reminder of the past.

The jewel in the crown of Big Bend is Emory Peak, rising to 7,500ft, and approached by a splendid walk on a fine path up through woodland to a high ridge and then a testing scramble to the summit. There are shorter walks such as that to the Lost Mine and longer ones such as the South Rim Trail, where one has a good chance of seeing bears, cougars and the javelina, a wild pig. Big Bend is actually a small US offshoot of the vast Mexican Chihuahuan desert and the ecology is unique.

It is rugged, desertified mountain country at Big Bend, but after driving eastwards you come to the rolling grasslands of the Davis Mountains State Park. This is an area which achieved a certain notoriety some years back when various heavily-armed right-wing supporters of Texas independence holed up and defied the government, leading to a shootout in which their leader was killed. The town of Fort Davis has good places to stay and eat, and also possesses Fort Davis, a former military post to protect the settlers going westwards from the Apaches after the civil war. It was however unique in that it was manned by Buffalo (black) cavalry and is worth a visit. But staying at the unique experience of Mount Davis Indian Lodge should not be missed. This was built by the Civilian Conservation Corps during the Depression in a modern adobe-pueblo style and is a great base for hiking.

Northwards and eastwards you enter flatter country, where cattle dot the landscape and share the emptiness with automatic fracking towers, pumping oil night and day. And the few towns are often staggering in the grandeur of their decay, like Pecos, once a bustling oil and cattle town, now consisting mainly of houses which are abandoned to dust and decay. Others shown on the map no longer exist at all. If you know your Larry McMurtry, this is the landscape of The Last Picture Show, novel and film.

And then, in the middle of nowhere you come across Pecos County Cowboy Church, a corrugated tin and clapboard shed. Peering in the dusty windows you realise that from way out beyond anywhere you can see, once a month, people come and congregate here for cowboy hymns and hot gospel – and for drinks at the cowboy bar. But soon the outline of a further range of mountains is discerned, 100 miles north on the horizon.

The Guadeloupe mountains are remote and camping aside there is no accommodation in or near the national park. Nights are chilly here in winter though days are warm. If camping doesn't appeal you can stay at Van Horn, about 50 miles from the Guadeloupes. Van Horn is a town that has all the Gothic splendour of rundown rural American backwaters, and was the setting for the 2005 film The Three Burials of Melquiades Estrada. It has yet another wonderful Trost-designed hotel, El Capitan, where, for a modest amount, you can stay in a tiled palace, a fountain plashing in the courtyard outside, listening to the lonesome whistle of the passing freight trains.

Most people come here to climb Guadeloupe Peak, which is – as almost always in US national parks – approached by an excellent, well-marked trail, rising through pinewoods to the summit ridge where a vista over the salt flats of the Texas desert is a thing of wonder. Intrepid travellers can embark on multi-day hikes through the back country of the park, again by marvellous trails. However, unlike at Big Bend, the weather can occasionally be ungentle here, with a higher likelihood of snowfall and, on occasion, high winds. For the lone winter traveller, day hikes are the best option. Again there are bears and cougars, but the likelihood of seeing one, still less of having an unwanted encounter with one, is very remote.

In far West Texas you can have the perfect American driving holiday, seeing wonderful country by day and being in your own movie at night, in splendid olde-world hotels. Trost me.

Ian R Mitchell is the author of Encounters in the American Mountain West, published by Neil Wilson.