We meant to go to Portugal in spring. We'd booked our tickets. Then something came up that made the trip impossible. Delta took $300 per person in fees and gave us the rest in vouchers that had to be used by year's end.

That $600 penalty burned. According to my vacation math, wherever we went now had to be cheaper than the original trip but even better. Meanwhile, airfares were soaring; prices to Lisbon had doubled. Flights to the other cities on our list — Quito, Santiago, Istanbul — cost even more.

Our anniversary was coming. My husband, John, voted to pitch the budget. But I was obsessed: I made a map of everywhere we could fly, currently, for the voucher price. Only one exotic, unexplored place popped up. That's how we ended up in Mexico City in fall.

It didn't sound romantic. Even veteran travelers gave us dire warnings about removing all our jewelry (including wedding rings) and updating our wills. But our marriage — every marriage, really — is based on risk. That's what I told myself in the taxi from the airport when the driver offered his services, just 5,000 pesos a day (about $250), to keep us safe.

We accepted his card, and he dropped us at the American brand-name hotel where all the websites we'd read advised we stay. It was musty and dilapidated and everyone was in character. Our concierge was dour and draped in black, his mustache pencil-thin. Our room was dark. A two-second alarm sounded every time the elevator descended to the lobby, making it hard for us to sleep.

The next morning, Sunday, we walked to Cafe Regina, a breakfast place tucked in a brick walkway that was recommended online. The forecast had been for rain every day but it was like no one told Mexico; we sat outside under a warm, clear sky and drank dark Chiapas coffees sweetened with honey. The building across the alley was covered with moss and 100-year-old bicycles that appeared to be driving up to the roof.

Older couples strolled slowly by, on their way to mass. Then I realized: Oh! They were our age, long-married people in their 50s. But different from us. Matching. The women and men tended to be around the same size; they walked easily arm in arm. There was a quiet dignity about the ladies with their rich eggplant-colored hair and brightly colored clothes. Few of them wore glasses. Unlike the American and European women I know, they seemed utterly indifferent to being watched.

John took my hand under the table. Silently, we agreed that we didn't need the taxi driver. We relaxed into the sunshine and ordered our second cups. At the far end of the walkway, the church bells began to toll.

It's important to mention that John and I do not match in that lovely Mexican way.

I'm a tiny, spectacled lady, barely 5 feet 3. I'm also halting in any language but my own. John is almost a foot taller than I, broad-chested, and so fluent in Spanish he acts as his high-tech company's consultant to Latin America.

When I say I felt safe in Mexico City, please take this into account.

That said, we behaved as we would in any densely populated place — London, Paris, New York. We stowed our passports and laptops in the hotel safe, stayed together and carried as little as possible on our walks around town. It helped that our mobile phone service was seamless.

Strange surprises

We'd done very little research before arriving. This is part of our risky vacation behavior: We like to show up in a place and let ourselves be guided. Occasionally this practice backfires. But more often, it results in strange surprises that delight us. So it was when we walked to the Zócalo and discovered a festival for Mexican Independence Day.

The holiday itself was days off — but this was the weekend and the entire city was celebrating under enormous spangling banners of red, white and green. There was a custom car show, an orchestra in the square, and a ceremony with young men in Aztec costumes smudging revelers in sacred smoke.

By 2 o'clock, we were exhausted. Mexico City is the 12th largest city in the world, with about 9 million people in the city center and 21 million in the greater metropolitan area. It is crowded in a way I'd never experienced; the streets teem with walkers, buskers and dogs.

We come from a place that's grown quiet with people lost in their earbuds and phones. Here, it was different: Everything happened out loud. The citizens love their music and blare it from every storefront. And this wasn't just patriotic mariachi; we heard George Michael, Latin EDM and Elvis all on one block.

The noise and smells and constant brush and dodge of people moving by overwhelmed us. In a habit that would become our standard for the trip, John and I went back to our hotel, closed the curtains for an hour and enjoyed the quiet. (Marred only by that eerie alarm.)

We spent that time reading about Mexican independence. I knew Spain had conquered the country at some point, but had never given a thought to who the people were before. A tribal nation, they were brutally colonized by Cortes' army in the 16th century. This explained so much: the art, the costumes, the unique mix of indigenous and European features that combined to create those small, elegant, impassive women I'd seen.

Great Goddesses

The next morning, we boarded a bus for a day trip to Teotihuacan. An ancient settlement 25 miles north of Mexico City, it has pyramids, caves and the ruins of a large civilization built around 100 B.C. Their deity was a Spider Woman called the Great Goddess of Teotihuacan.

We climbed the Pyramid of the Sun and then the Pyramid of the Moon. Connecting these is the Avenue of the Dead. Each structure is set in complex astronomical relationship to the sky; an Australian woman explained loudly to anyone who'd listen that it all had to do with equinoxes. But the truth is far more complicated than that.

What haunted me as we climbed sturdy 2,000-year-old stairs was the sense of real people inhabiting this place, precisely at the time of Christ. They worshiped a woman and a feathered serpent called Quetzalcoatl. And they understood the travel of the sun and moon in a way I can't conceive.

After another night at the American hotel, we took an Uber to Coyoacán, where the artists Frida Kahlo and Diego Rivera lived. Our driver wore a crisp shirt and tie. He handed us water as we entered his spotless car. The 40-minute trip cost 121 pesos, or $6.25.

On the way, he warned us to buy our tickets to the Blue House online. John pulled out his phone and confirmed our tour, just as we rode by hundreds of unticketed people waiting outside.

Our guesthouse in Coyoacán, Casa Aldama, was two blocks from the museum: a snug, fully outfitted two-story apartment in a compound circling a central garden with flowering trees.

I thought I knew Frida Kahlo, the anguished iconoclast who placed her own image at the center of her art. But that was nothing in the landscape of what we learned. Her mixed immigrant past, childhood maiming, inability to conceive, lifelong pain and love affairs with Diego Rivera, Josephine Baker and Leon Trotsky. This wasn't just about art but about politics, prejudice, social welfare, sexual liberation and disability.

From the Blue House we walked across town to Museo Anahuacalli, a glowering stone structure where Diego Rivera collected ancient artifacts. Here we were back to the Aztecs and the Mayans, the feathered serpent; this story circled back and took up where the pyramids left off. At the top of the gloomy building was a room with a sketch of Rivera's unfinished Rockefeller Center mural with hundreds of figures — from Roman emperors to eminent scientists to New York society ladies — that looked alive.

It was precisely then that dark clouds moved over the city and the only rainstorm of our entire stay commenced. We sat reading the story of how Nelson Rockefeller hated the commissioned piece because it showed a May Day Parade and Vladimir Lenin holding hands with laborers. Rockefeller demanded that Diego remove the portrait of Lenin; Diego refused but offered to add one of Abraham Lincoln, in balance. Instead, Rockefeller locked Diego out of the building and had the entire mural-in-progress destroyed.

Commerce, class warfare, censorship, science, money and art. Apparently none of this is new.

The span of human history

Back in Mexico City the following afternoon, we bypassed our "safe" American hotel. Instead, we had the driver drop us at the small modern Hotel Punto MX, a few blocks off the central square.

Here, we had a fresh, sunny, polished-clean room, a silent elevator, and a staff made up of welcoming and professional locals who greeted us each morning at breakfast and gave us common-sense advice.

"Take the subway!" said our concierge over coffee, when we told him we were on our way to the Museum of Anthropology. "Go five stops, to the grasshopper."

It was 5 pesos (25 cents apiece) for us to ride the subway. Be warned, the cars are body-to-body tight so the risk of pickpocketing or groping is increased. But the trip was quick. Each stop is marked with an illustration that everyone can understand. Ship, eagle, butterfly, bell.

We got off at the grasshopper and climbed a set of steps into Chapultepec Park — a Central Park-like green space in the middle of the city, surrounded by museums, playgrounds and cafes. It was a 20-minute walk to the National Museum of Anthropology, a stone and glass temple with wide open doors. The ticket taker waved us in.

"It is free today," he said. We never did find out why.

I don't know what I was expecting from a Mexican museum, but I'll sheepishly admit it wasn't this. The halls loomed around us. The same ticket taker walked up briskly.

"American?" he asked. I nodded, bracing myself for what he might say next. "Wait here." He pointed to a bench. "I will get you a tour."

Five minutes later a woman in uniform appeared. Her hair was burnished mahogany, her eyes sparkled and she carried a pointer, like a prep school instructor from 1915. She was perhaps 10 years older than I, and even smaller. But she walked with the bearing of an empress, pointer tapping the ground at her side.

"Come!" she said, after gathering a few straggling English speakers. "I will tell you about our history."

Not Mexican history, as it turns out, but shared history. The story started with Lucy, the first human whose bones were discovered in Ethiopia, and continued through early man's migration, the pyramids, indigenous cultures, Mexican warriors and European colonial wars.

At the mammoth carved sunstone, she paused to talk about numerology, weather, famine, agriculture, marriage, governments and gods.

"You see," she said, "when the Catholics came to convert the Mexican people, it was not difficult. They replaced each religious belief with another. The solstice became Christmas. The goddess became Mary. The story of this museum … " she waved her pointer in a circle. "It is that we people are really all the same."

Ann Bauer is author of the novels "A Wild Ride Up the Cupboards" and "The Forever Marriage."