Wyoming is a beautiful and unusual state, and America’s least populated, with vast tracts of uninhabited land. Some of the ranches are bigger than countries in Europe. And one of the main attractions for visitors (three million of them a year) is Yellowstone National Park.

It is a geothermal wonderland of mud pots, hot springs, fumaroles and, of course, geysers. It was the first National Park in the US, signed into law in 1872.

The park has eight main visitor areas with accommodation, information centres and museums. There are an almost overwhelming number of highlights, so I recommend looking at photographs first and deciding which attractions to see.

Black Rock in Yellowstone National Park

Devils Tower National Monument

I started my trip at the Devils Tower National Monument (apostrophe intentionally missing after a historical typing error!), a flat-topped igneous rock of mysterious origin, shaped like the underside of a mushroom.

It is a sacred worship site to Native Americans, who tie prayer cloths to trees around the base of the rock. And every June, it is closed to rock climbers, due to a month of Native American cultural activities.

In 1906, President Roosevelt established Devils Tower as the first national monument. However, more Americans know it from its appearance in Close Encounters of the Third Kind; there is quirky alien merchandise on sale at the nearby shop.

There is a gentle 1.3 mile hike around the base of the formation, or longer walks taking in the wildflowers and surrounding forest. It is a wonderful place for bird watching, viewing wildlife, and learning about geology and the indigenous people.

Scientists don’t agree on the origins of the mysterious Devils Tower

Yellowstone’s volcanos and hot springs

My first must-visit was the Grand Prismatic Spring, the largest hot spring in the US. Its sizzling colours topped with steam look like something Peter Jackson would have spent billions on special effects to produce.

I was wide-eyed and open-jawed at its surreal beauty (keep your wits about you, though, as the wooden walkways have no railings to protect visitors from the scalding water). Mammoth Hot Springs were another highlight. They look post-apocalyptic, or like a dream sequence.

The Grand Prismatic Spring, the largest hot spring in the US

The Yellowstone Caldera is a volcanic crater created by a massive volcanic eruption about 640,000 years ago. It’s the largest volcanic system in North America and the Yellowstone Volcano is still active, with thousands of small eruptions every year.

Countless other attractions that make the time, effort and money worth it include Artist Point, the Black Pool, West Thumb and the Fountain Paint Pot. It was worth finding out when Old Faithful’s famous cone geyser would next erupt, as every tourist seemed stunned by the show it finally put on.

When to visit Yellowstone

When to visit Yellowstone depends on what you want to see. In spring and autumn, there are fewer tourists and milder weather. Even in summer, the park can drop to freezing temperatures, due to the altitude, so do your research and come prepared for all climates.

Most tourists visit from May, when wild flowers and baby animals make an appearance, to October. Animal lovers will be enchanted by the 60 species of mammals in the park, including the grey wolf, lynx, grizzly and black bear, bison, elk and white-tailed deer.

Yellowstone has been nicknamed the American Serengeti as it contains the largest concentration of mammals in the continental USA. There are bison wandering around on the road, so patience is a virtue, and elk sitting in unexpected places, like the lawn of the park’s post office.

Be prepared to see bison roaming free (but be careful, they are wild)

Black bears coexist with grizzly bears (information if bears are a concern, though the odds of being injured by a bear are very low). Other potential dangers include bison – which photo-loving tourists run up to, unaware – and boiling water from geysers and geothermal basins.

Yellowstone is one of the most inspiring and beautiful places I have seen. Scientists, artists, nature lovers and even cranky teenagers brought along for the trip will be moved by the surreal, eye-widening delights.

The Yellowstone Terraces’ natural rock formations

Grand Teton National Park

If after Yellowstone you want more nature, visit the Grand Teton National Park, consisting of spectacular peaks rising along western Wyoming. If you don’t have the time or inclination (pun intended) to climb them, stop to take in the awe-inspiring view.

At the grand Jackson Lake Lodge you can have lunch and drinks in sight of the Teton Range and Jackson Lake, while marmots dart around nearby. If you love the ranges, spend a night or two at the lodge, which is registered as a National Historic Landmark.

The view from Jackson Lake Lodge

Travel to Wyoming

From the UK, fly into Denver, Dallas or Salt Lake City, then take a domestic flight to Bozeman or Billings in Montana, Jackson or Cody in Wyoming, or Idaho Falls in Idaho, depending on where you plan to start and the time of year.

From June to September, you can fly from Salt Lake City to West Yellowstone, Montana, a regional airport. See Yellowstone’s bus and train connections.

Getting around Wyoming

Hiring a car is ideal, if you’re willing to drive on the right and face bison and deer in the middle of the road. Otherwise, join a tour. If you’re particularly daring, join a six-day horseback tour around the state. More information on Wyoming Tourism and Wyo.

Where to stay and eat

Yellowstone: Hotels, lodges and campsites in Yellowstone. The historic Old Faithful Inn is notable. Restaurants include the rustic Roosevelt Lodge and the environmentally conscious Mammoth Hot Springs Dining Room. Book hiking tours or horseriding tours.

Grand Teton National Park: Find accommodation in the park. Of all the eco-friendly lodges, Jackson Lake Resort is the largest, and a base for numerous activities. Restaurants include Jackson Lake Lodge Pioneer Grill, a 50s-style diner