AMERICAN BANKROBBERS talk of escaping south to Mexico, or north to Canada. In life, some of them might actually make it. In movies, they never do. Either way, those fugitives are betrayed by the limits of their imagination. Anyone who is serious about disappearing dreams of Alaska, a place so far from everywhere else that it is still possible to doubt its existence, and which many Americans don't know or believe belongs to the United States.

Most of the half-million or so people who now live in the 49th state (which is referred to as a state of being as well as an official designation - this vast space was purchased from Russian commercial interests in 1867, but only joined the union in 1959) have run from what they call "the lower 48". The majority have settled in Alaska's cities and towns, but even the biggest of these appear as provisional points of electric light against immense surrounding galaxies of trees, rock, ice and blue water.

Juneau, the capital, cannot even be accessed by road. But boats and planes - and floatplanes, those essential Alaskan combinations of the two - can also take you much further out, to tiny stations of hospitality known as wilderness lodges, where the supply lines of civilisation somehow extend beyond basic accommodations to provide gourmet cooking and luxury down duvets. Here are three of the best.

WATERFALL RESORT, PRINCE OF WALES ISLAND This former cannery, a short flight by floatplane from the rain-soaked, tourist-friendly mini-city of Ketchikan, has become a world-renowned fishing lodge, where captains of industry compete with an attitude more businesslike than sportsmanlike to catch the heaviest king salmon of the season. It is consoling to know, as I retch over the side of a boat near the aptly named landmark South Bobs, that regular visitors, and even native Alaskans, suffer constant waves of travel-sickness because of their reliance on flimsy and windblown modes of transport. Later - far too late - at tonight's buffet table, someone recommends a mixed dose of Antivert and Sudafed, but for now I try to transcend the nausea by meditating on nature between heaves.

Through watery eyes, I watch a bald eagle fly along the treeline, seize on a perch with his claws, and stare right back at me. I am told that America's national bird is considered less magnificent up here. "In Alaska," says boat captain Mike King, "eagles are like seagulls at the dump." Speaking of the dump, the resort's general manager DJ Heiser says casually that I might meet a bear when I try to recover my legs by walking out to the waterfall, past the spot in the forest where they burn rubbish.

I do. He's right there. The bear is black, and therefore smaller than Alaska's more famous and fearsome brown "grizzlies", but he looks substantial enough, even while scavenging in the smoke. He stops and stares at me, too, considering his options. Then he moves off, without haste, making the trees wobble in his path. I only get scared once he's gone.

Waterfall Resort, 001 800 544 5125, www.water fallresort.com. Prices start from about £1222 for a three-night, four day all-inclusive package.

FAVORITE BAY LODGE, ANGOON The Chatham Strait, around Admiralty Island, is a thoroughfare for humpback and killer whales. From the window of an Alaska Seaplanes aircraft 1000ft overhead, I see one of those long shadows breach clear out of the water. The other five passengers don't notice, and the engines are so loud I don't tell them.

When we land at Favorite Bay, we are met on the dock by Gil Lucero, a former champion bull-rider and movie stuntman who first came here on a bear hunt with the hard-drinking cowboy actor Slim Pickens (the island is home to the largest concentration of grizzlies in the world), and became a handyman when Dana Durand arrived to build his dream lodge seven years ago. Inside the wooden structure itself, which has been custom-fitted with antler chandeliers, native Tlingit tribe totems, and expensive bedding, French chef Pierre Coutou is waiting with a silver tray of hot chocolate-chip cookies.

We spend the next day with well-armed and highly educated guide Brandon Cullum: fishing, kayaking, hauling heavy crab-pots up on to his boat, and hiking warily through deep woods that will, later be described, in all seriousness, as a "bear's living room" by the lodge's in-house butler Roger Wark over a fresh, rich seafood dinner.

The comforts on offer within these cedar walls are made dissonant by thoughts of the primeval world outside, and mitigated by an awareness of the modern poverty down the road in the town of Angoon, which was once the seat of Tlingit power and culture but has since been run down by every social problem that now besets America's indigenous populations.

Favorite Bay Lodge, 001 866 788 3344, www.favoritebay.com. Prices start from about £1700 for a three-day, three-night all inclusive package.

AFOGNAK WILDERNESS LODGE, SEAL BAY, KODIAK Roy Randall built this homestead with his bare hands, on the site where he stopped to skin a seal in the 1960s with his hunting buddy and Hollywood namesake Roy Rogers. Now he and his family - wife Sharon, sons Luke and Josh - run an operation which will ensure their survival after doomsday, complete with generators, a sawmill, a fish processing plant, and a fully stocked armoury. Sharon expects that day soon, without doubt or worry.

Her religiosity is perhaps partly explained by the glories of the place where the Randalls have a made a life, amid small islands which form a kind of northern Galapagos. Within minutes on a single sunny day - rare enough around here, where clouds and fog often reduce vertical and lateral visibility to "zero and zero" - Luke can manoeuvre his boat to show you whatever you would wish to see in Alaska. A rock occupied by roaring sea-lions. A log cabin, unoccupied for the past decade, where passing hunters still leave friendly notes for the owner. A humpback whale and her calf spouting alongside us.

And there, on the beach at Perenosa Bay, three Kodiak brown bears - the biggest in the world - standing in sunbeams at nearly midnight. To those who have never seen one before, grizzly bears are mythical beasts. Watching them with your own eyes in the wild, they become more so, not less.

Afognak Wilderness Lodge, 001 907 486 6442, www.afognaklodge.com. Prices are approximately £375 per day, all inclusive.

HOW TO GET THERE Fly from Glasgow to Ketchikan or Anchorage via London Heathrow and Vancouver or Seattle with British Airways (www.britishairways.com) and Alaska Airlines (www.alaskaair.com) from £575 return.

FURTHER INFORMATION Check www.travel-alaska.co.uk.

CARBON FOOTPRINT Approximately 2.31 tonnes CO2 on a return flight from Glasgow via London and Seattle.