But you need only drive a few yards further to the log-cabin welcome station to discover that at this park, as at dozens of others across the nation, all is not well. Down the list of the park's facilities two freshly- painted "closed" signs are posted. A story in the give-away park newspaper ominously trumpets: "Yellowstone National Park: just one step from insolvency".
The parks are basically broke and this summer, when the tourist swarms are at their peak, visitors are for the first time being forced to take notice. Campgrounds, trails and other attractions are closed, rangers are fewer in number and roads are crumbling beneath the rush of cars and mobile homes. The picture is the same whether you are here or at Yosemite, Glacier, Grand Canyon, or any of the scores of lesser-known parks across the country.
One obvious culprit is the low entrance fee. At Yellowstone a carload of passengers will pay only $10 (pounds 6.50) for the privilege of touring the park for a whole week, not a cent more than when the park was established in 1916.
More critical, however, is the squeeze being applied by the politicians in Washington, who, in their frenzy to wean all dependents of the state from federal funding, have seen little reason to exempt the parks. Since 1993 the system's budget in real terms has dropped by $202m, or 17 per cent.
No park has stirred more controversy than the most famous, Yellowstone. After briefly considering the closure of a large part of its territory, the park opted to close a museum and campground at its second-most visited geyser area, the Norris Geyser. The move provoked fury from state politicians in Wyoming who were worried about tourist revenue, while visitors to Norris constantly express dismay.
"I just think that this is very, very sad, it really fries me," comments Kurt Speidel, a California schoolteacher, pausing outside the closed doors of the Norris museum. "This park is part of our diplomacy, people come from all over the world to see it. And what they find is this - because the Republican politicians think the park is good enough as it is, and go visit their fancy guest ranches instead."
Don Striker, Yellowstone's embattled budget director, understands the bitterness but makes no apology for the closures, which may, after all, send a message about the depth of the park's plight. "We've been dealing with this more or less invisibly for a few years already but this year we just hit bottom," he said. "Maybe there is an element of political statement in this, but it was definitely time to let people know what is happening".
Congress, meanwhile, does have some ideas on how to save the parks. One bill under consideration would allow them to set entrance fees, and presumably raise them. A second, which has the support of President Bill Clinton, envisages a more radical step towards privatisation. For the first time it would allow limited forms of corporate sponsorship for the parks. Advocates of sponsorship say it would raise an extra $1bn for the system over 10 years and could be managed tastefully.
The current proposal, for instance, suggests that only 10 corporations would have the chance to become "sponsors" of the parks. They would be barred from displaying their logos within the parks but could plug their support for the parks in their advertising campaigns. The pay-off for the companies would be public goodwill for their show of generous altruism.
Critics believe the plan would be the thin end of the wedge, however. Pointing to the corporate overload currently on display at the centennial Olympic Games in Atlanta, where Coca Cola and Visa are vying with the athletes for the world's attention, they envisage such horrors as "Old Faithful, brought to you by the battery that just keeps on going", or, "The Disney Grand Canyon".
"It would certainly help," says Mr Striker of the sponsorship plan, before adding: "But you don't want McDonald's emblazoned on the bison".
Jeff Dean, another disgruntled visitor at the Norris area, goes further: "Old Faithful is brought to us by nature, it is not brought to us by some company."
Another concern is that while corporations might be happy to bankroll the most famous of the parks, they would have no interest in maintaining the less visited ones.
All told, the parks say they face a combined cash shortfall of $4bn if all urgent maintenance projects are undertaken. The Grand Canyon National Park has already formally declared itself bankrupt while the Timpanogos Cave National Monument in Utah has said it will turn away up to 10,000 visitors this year because it has no rangers to guide them. Some in Congress, meanwhile, are debating a third bill to begin the process of stripping the national park designation from some parks which are considered least worthy.
There is one other possible scenario for salvation: a return of Democrat majorities in the Congress and some moderation of Washington's current budget-cutting frenzy. Failing that, there may be still more engraving to be done on Yellowstone's north arch: the addition of a smiling Mickey Mouse.Reuse content