CODY, Wyo. — You know western Wyoming and dumb luck are both on your side when:

—Your daughter spies three mule deer in a Yellowstone meadow. Then a moose mid-river. Then bison, fox and marmot, trumpeter swans, a wayward seagull and a grizzly family — mama bear and two cubs, romping across the high slopes, safely distant but still riveting.

––You hear the word "rodeo" used as a verb. Then you attend one in Cody, about 50 miles east of Yellowstone, and see not only bucking broncs, bull-riding, barrel-racing and calf-roping but also a stunt rider who circles the ring while standing astride two galloping horses.

––You look up from lunch at Buffalo Bill's old hotel and find that Miss Rodeo Wyoming is seated at the counter, right between Miss Cody Stampede and Miss Rodeo America, all chowing down in their spangled blouses and sashes.

––Old Faithful, which generally rests for 90 minutes between eruptions, starts spouting the moment you step up.

––The Old Faithful Inn, whose dinner tables are often booked months in advance, has space for you the moment you step up. (It helps to step up at 10 minutes before 5 p.m.)

––On a foray into Yellowstone's Mammoth Hot Springs area, you discover an appalling array of tasteless lawn ornaments at the home reserved for the Yellowstone concessionaire's top executive. Then they move, and you realize the elk are real. All 10 of them. They can't resist the grass and shade, the camera-happy tourists can't resist the elk and the rangers are forever struggling to keep the beasts with antlers separated from the beasts without.

OK, by now, you've realized this isn't a multiple-choice test. It's more a reminder: Even when fully besieged by the summering masses, Yellowstone National Park remains a wildlife parade, a geothermal freak show, an essential rite of North American tourism, a lot of fun. And a side trip to Cody can fit about as nicely as cornbread alongside a slab of ribs.

In early July, my family and I spent five days in tiny Cody and massive Yellowstone, whose 3,472 square miles cover much of northwestern Wyoming, spilling over into southern Montana and eastern Idaho. The park — which became the first national park in the world when it opened in 1872 — had nearly 3.3 million visitors in 2009.

That was a record, but with so many Americans reconsidering foreign travel, packing up cars and heading for the parks, it might soon be broken. Yellowstone spokesman Al Nash says June was the busiest ever at the park: 694,841 visitors in 30 days. For at least a few nights of our visit, every one of the more than 2,000 hotel rooms and cabins in the park was booked.

That means a lot of traffic along the park's 142-mile, figure-8-shaped Grand Loop Road, especially with so many animals afoot this summer, nibbling the generous growth after a wet spring. On Aug. 25, the park will add one more enticement by replacing a batch of temporary buildings with a new $26-million Old Faithful Visitor Education Center, replete with green construction elements and exhibits to show how and why the earth here spits hot water skyward.

If you enter the park from the south, the drama starts right away, with the steep slopes down to the Lewis River, the racing water and the ridgelines crowded with charred trees remaining from the fires of 1988. An estimated 36 percent of the park burned during that dry summer, and legions of skeletal lodgepole pines endure, dead sticks standing. But two decades of regrowth have brought along another generation, shorter and greener, putting visitors in the middle of an epic reminder that death and rebirth are natural neighbors.

We knew to expect big crowds and occasional traffic jams (some caused by roadwork, most caused by gawking drivers and meandering park mammals) so we didn't mind them. Like generations of families before us, my wife, Mary Frances, and our 6-year-old, Grace, opened a notebook to count sightings of critters. Fearing the "Mona Lisa" effect ("But it's so small!"), we didn't expect much from Old Faithful. But when the geyser immediately leapt into action, about 100 feet high and surrounded by perhaps 1,000 expectant visitors, there was no time for letdown. We took in the spectacle and sulfurous scent for perhaps five minutes, then marched right along to the Upper Geyser Basin, following boardwalks past scores of geothermal features, from eerily colored pools to mini-mountains spouting towers of spray.

"It smells like Milo," said Grace. (Milo is a 12-year-old yellow Lab with occasional gastric issues.)

Until you get here, it may be impossible to appreciate all the ways that water rises, falls, rushes, rests, is cooked, is chilled, is channeled and is flung in Yellowstone. There are more than 300 geysers and almost as many waterfalls, including the roaring wonders known as the Upper Falls and Lower Falls of the Grand Canyon of the Yellowstone.

Watching Lower Falls, Tim Cahill writes in his book on Yellowstone, "Lost in My Own Backyard," is "like watching a fire: the same thing keeps happening and happening, but just a little differently every time, so that it holds the eye and empties the mind."

So we risked vertigo and took the half-mile switchback trail down to the Brink of Lower Falls. Spellbinding. Then we took the easy strolls to Inspiration Point and Artist Point — two more postcard views. The steeply pitched canyon may be only about 20 miles long, but to paraphrase Richard Nixon's assessment of that wall in China, it is grand indeed.

It might be perverse to think too hard about man-made objects in such a place, but we spent more time admiring architecture than we expected to, beginning with the Old Faithful Inn, a century-old marvel with a six-story lobby, steeply pitched roof and a 500-ton stone fireplace and chimney. This is where the semi-rustic, lodgepole-pine-intensive genre of "parkitecture" was born, and once you're inside, it's difficult to leave.

Under its spell, we found our way to two other woodsy wonders: the Roosevelt Lodge, which is north of the park's most heavily trafficked areas (and served me a memorable elk empanada), and the Lake Lodge, which faces Yellowstone Lake and offers cafeteria food under soaring pine ceilings.

We saw the Yellowstone Lake Hotel too, from its yellow walls to a set of Greek Revival columns that would fit right in on a Louisiana cotton plantation. Even though it's been well-restored, the place felt cold and lonely at lunchtime, much of the wicker lobby furniture empty, and I couldn't get out of there fast enough. Yet the same architect, Robert Reamer, designed the Old Faithful Inn and the Lake Hotel's exterior. And he did them at more or less the same time, in 1902 and 1903.

As it happens, Reamer also designed much of the Mammoth Hot Springs Hotel at the northern end of the park, where we spent two nights. It was an adequate place to stay, its smallish rooms lined up above a modest lobby, just five miles from the gateway town of Gardiner (where the nonprofit Yellowstone Association. opened a handsome store and visitor center in May 2009) but far from most of the park's most popular features.

Like the park's other hotels, the Mammoth Hot Springs has no TVs and no air conditioning. It hasn't even switched from metal keys to keycards, and our $117 room had no closet, no bathtub, no rollaway bed available. But in summer, the elk are everywhere — not only outside the concession chief's residence, but on the grass behind the Terrace Grill, at the door of the general store and around the otherworldly terraced calcium carbonate formations for which the area is named.

One day we made the mistake of bragging to another family about how many elk we'd seen. A boy of about 10 gazed back, unimpressed.

"We've seen 78," he said.

OK, never mind.

Next stop: Cody

Of course we could have stayed longer, seen more of Yellowstone, devoted a few more hours to Grace's education in the fine art of stone-skipping. But Cody was calling. Cody, the town founded in the 1890s by the great Western showman Buffalo Bill.

Set on the windswept plains just east of the mountains, Cody (elevation 5,095 feet; population, about 8,800) sits along the northern fork of the Shoshone River. To reach it from Yellowstone, you drive along the river as it rushes beneath the dramatic slopes and buttes of the Wapiti Valley.

Cody trades on its Old West roots, but it hasn't been infiltrated by galleries and fancy restaurants in the manner of Aspen, Colo.; Ketchum, Idaho; or western Wyoming's own glamour capital, Jackson Hole, about 50 miles south of Yellowstone. I liked that about Cody. I especially liked the Nite Rodeo, a family-friendly spectacle that unfolds every summer evening as the sun slowly ducks behind a ridge at the western end of town.

We plopped down $20 a head and went our first night here. It's a profoundly local event (Denny's Guns & Maps sponsors one of the chutes) yet draws global audiences, including domestic travelers like us and foreign visitors like the unaccountably cranky French couple in front of us and the merry family from the Indian subcontinent that arrived just ahead of us. Then the chutes opened, the animals jumped and the cowboys lurched. And up in the stands, there were no discernible drunks. How do you throw a sporting event, enlist a beer company as a co-sponsor and keeping drinking to a minimum?

The next morning, after the town's Independence Day parade, we sauntered into Buffalo Bill's Irma Hotel, Restaurant & Saloon, built in 1902, with additions in the '20s and the '70s. That's where we spotted the rodeo queens, Kiley Boe (Miss Cody Stampede), Erin Heffron (Miss Rodeo Wyoming) and Kelli Jackson (Miss Rodeo America), tucking into their lunches at the old cherry wood bar, the blankly staring moose heads, tin ceilings and antler chandeliers arrayed above. Our lunch was fine, but the atmosphere — part-hokum, part-frontier legacy — was the treat.

Just outside the Irma, shootouts are staged six nights a week in summer, no charge. (Just imagine, Angelenos: a town where gunplay is good for business.)

We missed the gunfight, because the indoor pool at the Cody, our very comfortable hotel, was beckoning. But there was no way I was going to miss the Buffalo Bill Historical Center.

The center is not one museum; it's a complex of five. One explores Buffalo Bill's history as a global Wild West Show impresario and maker of frontier myths. The others cover the art, natural history, Native American cultures and weaponry of the West, and there's nothing small-town about them. They tell compelling stories with striking and extensive collections, including plenty of paintings by Thomas Moran, Charles Russell and Frederic Remington in the art space, and a circular natural-history exhibition space (completed in 2002) that leads visitors on a spiral journey through the flora and fauna found at different altitudes. With time for lunch in the cafe and a stroll through the sculpture garden, the center itself will likely fill most of your day.

But there was one more rendition of cowboy history in Cody that I wanted to sample. On our last morning in town, while the girls readied for the trip home, I crossed the street from our hotel and spent a few minutes wandering through Old Trail Town, a collection of more than two dozen historic log cabins from all over the state. There's a schoolhouse, a store, an Indian scout's house and a grave monument to 19th century trapper John Jeremiah "Liver-Eating" Johnson (sometimes rendered "Johnston"), inspiration for the 1972 Robert Redford film "Jeremiah Johnson." There are also two cabins that apparently housed Butch Cassidy and the Sundance Kid between bank robberies.

For a while on that slow morning, I was the only visitor, the boardwalk creaking underfoot. Trail Town was as dry, still and empty as the summery Yellowstone was green, mutable and crowded. You know your luck is holding when the West gives you such yin and yang, all in a single corner of Wyoming.

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