1. Walk in the parks

There are so many spectacular walks in Alaska; the challenge is working out which ones to pick. Ramblers Holidays (ramblersholidays.co.uk) has a 13-day itinerary of full-day walks, mostly rated moderately challenging, but also including steep ascents and rough paths in remote areas. Travelling in maximum group sizes of 12, the tour focuses on classic national park regions, and a trip highlight is the strenuous 10-mile Harding Icefield Trail, near Seward, with its close-up views of glacial cracks and crevasses.

Alaskan Wilderness Walking and Wildlife from £5,399, including flights, transfers and most meals. Departs July 11 and Aug 22.

More travel ideas and destinations to look forward to

2. The scenic route

If you prefer not to drive yourself, an escorted coach tour is a more relaxing way to cover ground with the added bonus of a knowledgeable guide on board. Titan’s (titantravel.co.uk) 12-night trip includes scenic drives through the country's most spectacular landscapes, plus city tours of Anchorage and Fairbanks, a cruise on a Fairbanks stern-wheeler to visit an Athabaskan Indian village and an excursion to the Alaska Wildlife Conservation Centre in Portage Valley.

Natural Wonders of Alaska from £3,349. Includes flights, transfers and rooms. Departs May to August.

3. Coastal cruises

Many cruise ships make the journey from Vancouver, northwards through Glacier Bay before winding up the voyage in Seward. Scenic's (scenic.co.uk) 14-day itinerary combines this iconic voyage with a tour of inland Alaska including a rail journey from Talkeetna, a stay in the Denali National Park and a flight over the Arctic Circle from a riverside lodge in Fairbanks.

Alaska including the Arctic Circle from £5,595, including flights, transfers and most meals. Departs May, July and August.

4. Bear necessities

More than 13 million acres of Wrangell-St Elias comprise the largest protected area of national park in the world. Natural World Safaris (naturalworldsafari.com) arranges stays here based at the remote Ultimate Thule Lodge, and excursions further into the wilderness by light aeroplane. As well as the vast glaciers, you may see bison, moose, black bears and wolves on the high alpine tundra. The family-run lodge has a wood-fired sauna and hot tub, and accommodates up to 12 guests in large, private cabins.

The Best of Wrangell-St Elias from £6,255 for five nights, full board, including transfers but not flights. Departs year round.

5. Back-country camping

A camping expedition through one of the world's remaining wildernesses is not for the faint-hearted. Grand American Adventures' (grandamericanadventures.com) two-week tour includes a seaplane trip to search for black and grizzly bears and a chance to watch the Pacific salmon on their annual spawning run. Also on the itinerary is a ferry trip through Prince William Sound from Valdez, home to harbour seals and sea lions.

Alaska, Wildlife and Wilderness from £3,419, including all meals. Excludes flight and transfers. Departs June to August.

6. National parks

There are few more remote and scenic landscapes than Alaska's mountains, rivers and lakes. If you want to really engage with the wilderness, then World Expeditions (worldexpeditions.com) offers a tour that includes hiking, kayaking and rafting, with accommodation in simple but comfortable hotels, lodges and cabins. Among the highlights is a canoeing trip in the tundra foothills of the Tangle Lakes, a challenging trek in the Chugach Mountains and a scenic bush flight into Wrangell-St Elias National Park. An introductory ice-climbing course on Kennicott Glacier is an optional extra.

Great Alaska Adventure from £3,400 for 10 nights, half board. Excludes flights and transfers. Departs June to August.

7. Motorhome and away

Nights will be chilly, but in July and August daytime temperatures can reach 22C in some areas of inland Alaska, with long hours of daylight, so motor-camping can be a good way to explore. In the peak season months, Discover The World (discover-the-world) offers a self-drive motorhome itinerary in vehicles, which can sleep from three to seven people. A package covering 1,500 miles is included in the price and a suggested circular itinerary departs from Anchorage and follows the Parks Highway through the Denali State National Park to the city of Fairbanks.

Alaska by Motorhome from £1,120 for 11 nights for a standard C25 motorhome, sleeping up to five. Excludes flights and transfers. Departs May to September.

8. Polar Bear Boating

Polar bears are largely solitary animals and their whereabouts often hard to predict. Biologist and tour operator, Allan Blanchard, of Wildlife Trails, collects data on their movements to predict when to travel for the best sightings in the Kaktofick region in the High Arctic. Staying in a small Inupiat community, these trips include three days of small-boat safaris into sheltered inlets, on board a 24ft vessel with an enclosed cabin and enough deck space to accommodate six.

Polar Bear Tour to Alaska from £3,530 for six nights, including all meals. Excludes flights and transfers. Departs August to October (wildlifetrails.co.uk).

The Sunday Telegraph