Yellowstone, Grand Teton and Mount Rushmore, 5 Nights

A private driver meets your flight at Jackson Hole airport, which lies within Grand Teton National Park, and takes you the short way into town. The rest of the day is free. Walk the boardwalks around the town square with its arches of elk antlers, and watch the evening light on the mountains. In winter the National Elk Refuge just outside town fills with thousands of elk.

Breakfast, then an early start north into Yellowstone. The guide carries binoculars for spotting wildlife, and the day takes in Old Faithful and its geyser basin, the Grand Canyon of the Yellowstone with its two waterfalls, and the wide grassland of Hayden Valley, where bison graze close to the road and wolves or grizzlies are sometimes seen at a distance. Back to Jackson in the evening.

Breakfast, then most of the day inside Grand Teton, where the peaks rise sharply from the valley floor. The tour usually visits Jenny Lake and Jackson Lake, the river bend at Oxbow where the mountain reflects on still mornings, and the old barns of Mormon Row. Watch for moose in the willows along the rivers, and for pronghorn, the fastest land animals in North America, on the sage flats.

Breakfast and check-out, then a private transfer to Jackson Hole airport for the flight to Rapid City, South Dakota, which usually connects through a hub. A driver meets you on arrival. In the evening, walk the downtown streets, where bronze statues of past presidents stand on the corners, or, with time and energy left, take a taxi or a transfer booked at extra cost out to Mount Rushmore after dark, roughly forty minutes away. From late May to the end of September a ranger-led evening programme ends with the carving being lit; outside that season it is simply floodlit after sunset.

Breakfast, then a full day in the hills. Mount Rushmore comes first, when the sun lights the four faces, with time for the walk below the sculpture. The Iron Mountain Road winds through Custer State Park, where bison and wild burros roam and lunch can be bought. Then the granite pinnacles of Needles Highway, the mirror-still Sylvan Lake, and finally the Crazy Horse Memorial, still being carved from its mountain.

Breakfast and check-out, then a private transfer to Rapid City airport for your onward flight. With a late departure, Badlands National Park is about an hour east, with eroded striped buttes and prairie dog towns, and can be added as a private morning excursion if you tell us when you book.