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 basically 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 plain 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 and was fully booked, 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 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 Assn. opened a handsome store and visitor center in May 2009) but a hefty distance from most of the park's most popular features.

Like the park's other hotels, the Mammoth 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.

Of course we could have spent 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., or 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 west 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 café and a stroll through the sculpture garden, the center will likely fill most of your day by itself.

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 made ready for the trip home, I crossed the street from our hotel and spent a few minutes wandering amid weathered lumber of 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.

chris.reynolds@latimes.com