You’ve got to love a country where a 16th-century martyr, a soccer star, a leading politician, and a brewery share a name. Cuauhtémoc, the last Aztec emperor, was tortured and killed by the Spanish on charges of treason. Modern Mexican sports fans got plenty of satisfaction in their lust for goals when futbolista Cuauhtémoc Blanco was a member of Club América, which won the CONCACAF Champions’ Cup in 2006. (He now plays for the Chicago Fire.) Cuauhtémoc Cárdenas, former mayor of Mexico City, still has hopes of following in the footsteps of his father, former Mexican president Lázaro Cárdenas. And Cervecería Cuauhtémoc Moctezuma needs no introduction to anyone who’s ever beaten back a hot afternoon with a cold Dos Equis or Tecate.

Home to a vast collection of physical remnants of North America’s past, Mexico has an enviable sense of connection to its heritage. And in many sites, whether they’re prehistoric, pre-Columbian, colonial, or cutting-edge, the built attractions have to compete for attention with the great natural beauty of their settings.

Cabo San Lucas

Baja California Sur, the 600-mile stretch of Mexico occupying the lower half of the Baja California peninsula, has been captivating wildlife enthusiasts for some 7,500 years. We know this because at least that long ago, residents of the region claimed caves, cliffs, and rocks as rudimentary art surfaces, capturing images of local birds, animals, and fish. Preserved in a dry climate, the paintings retain their vibrant colors and remain fascinating both artistically and logistically, as no one has yet figured out how the artists reached some of the surfaces they painted. UNESCO, which added the works to its World Heritage Site list in 1993, calls them “one of the most outstanding collections of rock paintings in the world.”

Golf courses — many with holes overlooking the Sea of Cortés — line the coast along the southernmost part of the peninsula. Even if the highway signs all disappeared, you could probably find your way from Cabo San Lucas to San José del Cabo just by following the trail of golf courses. In Cabo, you’ll also find some of the world’s finest deep-sea fishing along with activities ranging from sailing, diving, snorkeling, and waterskiing to mountain biking, horseback riding, and paragliding. Throw an array of luxury resorts and dining and nightlife options into the mix, and you’ve got one of Mexico’s most popular vacation destinations.

Oaxaca

The best advice any first-time visitor to Oaxaca can receive is to arrive with an empty stomach and an empty extra suitcase. You’ll find plenty here to fill both.

The Metropolitan Cathedral, which overlooks the
zócalo in Mexico City

Oaxaca is the home of one of Mexico’s most celebrated regional cuisines. Just setting out to try all the local variations on mole can be a mission in itself. Got a palate that craves something more adventurous? Head to one of the city’s open-air markets to grab a bag of chapulines, fried grasshoppers. Choose the smallest ones for the crunchiest snack, the largest if you prefer something chewy.

As for that extra suitcase, you’re going to need it. Oaxaca is renowned for its handicrafts. This is the place to shop for handwoven rugs and wall hangings, black pottery ceramics, mirrors with magnificent hammered tin frames, and the fanciful carved wooden animals known as alebrijes.

It’s all enough to rival the sightseeing. Within the city itself, the Iglesia y Ex-Convento de Santo Domingo is a spectacular example of the gilded extravagance of the colonial period. Don’t miss the Museo Rufino Tamayo, which features a very different collection from the museum of the same name in Mexico City. Here you’ll find Oaxaca native Tamayo’s personal collection of pre-Hispanic artifacts. Leave time to stroll the streets in the city center, listen to an impromptu concert by musicians stationed in the gazebo on the zócalo (the town square), and, if you’re a dance fan, catch the Guelaguetza festival dancers in performance at the Hotel Monte Albán, located right on the zócalo.

Chihuahua

Chances are good that if you’re in Chihuahua, you’ve either just arrived from Sinaloa on the Chihuahua al Pacífico Railway or you’re getting ready to board the train for the Pacific coast. The railway’s 415 miles of track pass through 87 tunnels and over 37 major bridges that make possible its passage through the Copper Canyon.

But Chihuahua itself is a city rich in colonial architecture and revolutionary history. Father Miguel Hidalgo, whose call to arms launched the War of Independence on September 16, 1810, was executed in Chihuahua the following year. The Calabozo de Hidalgo, the dungeon where he was held, is a tourist attraction whose displays include the priest’s pistol, crucifix, and personal letters.

Also in Chihuahua is the Museo Histórico de la Revolución Mexicana, housed in the former mansion of made-for-Hollywood Mexican revolutionary Francisco “Pancho” Villa. The museum’s exhibits mix the historical with the macabre. Visitors get a glimpse of various rooms in the home that show what life was like in Mexico a century ago. They can also see the Dodge in which Villa was riding when he was assassinated. The bullet holes in the car have a companion in the one clearly visible in the forehead of Villa’s funerary mask, also on display.

Mexico City

Huge almost beyond conception, teeming with more than 8 million residents, Mexico City is just outsized enough to be able to hold pieces of the country’s entire history.

The zócalo, in the city’s historic district, almost accomplishes that feat on its own. Here, the remnants of the Templo Mayor of Tenochtitlán stand in the shadow of the towering Metropolitan Cathedral, which was built with stones taken from the Aztec city the conquistadors had reduced to rubble. Next to the cathedral is the National Palace, which visitors can enter to tour a multistory series of Diego Rivera murals depicting Mexico’s past.

Also in the historic district, roughly a half mile from the zócalo, is the Palacio de Bellas Artes. Part concert hall, part museum, the majestic building houses exhibition galleries, iconic sculptures, and stirring murals by Rivera, José Clemente Orozco, David Alfaro Siqueiros, and other Mexican artists. Within the theater, the crystal ceiling depicts Mount Olympus, Apollo, and the Nine Muses. And this may be the only performance space in the world that rewards gazing at the curtain: the enormous work, designed by Tiffany & Co., offers a view in stained glass of the lakes and volcanoes of the Valley of Mexico.

The Palacio stands to one side of the Alameda Central, a park bordered at the opposite end by the Paseo de la Reforma. That grand boulevard will take you past monuments to Christopher Columbus and Cuauhtémoc, through the chic shops of the Zona Rosa, and on to Chapultepec Park, home to several museums. It’s all proof that Mexico City draws on a rich heritage and yet is firmly in the vanguard.

Getting There: Continental offers service to 31 destinations in Mexico, more than any other carrier.