As we float down the canal in Xochimilco, our multicolored boat jostling with dozens of others just as bold and brash, we can feel Mexico City’s past and present. Being on the water was the norm in the Aztec days, when what’s now the city center was a grand island in a lake. Around us, though, it can only be Mexico in the here and now, with vendor boats sidling up to sell michelada, spicy beer cocktails, and boats with mariachi bands playing the crowd favorites with gusto.

Like the capital city itself, this trip down the canals is chaotic and boisterous. Some couples are in their own private boats, sharing a romantic birthday or anniversary trip, serenaded by a trio of musicians. A few boats lashed together have turned into party barges, with bottles of tequila making the rounds, while others are filled with extended families adding ice cream from passing vendors to their own bounty.

This unlikely city has been a leap of faith from the start, built on an expanded island by nature-taming Aztecs, then with more filled-in land as it became the capital of the New World under Spanish rule. Through earthquakes, sinking foundations, pollution problems and a crime wave in the 1990s, it has somehow not just endured but boomed. It’s the hub of an economy that keeps moving up the list of the 20 largest in the world.

By most estimates, the statistical metropolitan area is the second-most populated city after Tokyo. This is misleading for visitors, however. Just as most couples coming to New York City on vacation never set foot in Queens or the Bronx, most tourists visiting the D.F. (Distrito Federal) tend to only move in a well-defined area. That defined area can be a quite enchanting space. Starting from the rejuvenated colonial center, anchored by the huge Zócalo plaza and stretching to chic Polanco and Chapultapec Park, this is a Mexico City that leaves many visitors wondering what took them so long to get here.

Old reputations die hard, though, and D.F. still conjures up fears of danger, even though local residents will tell you they haven’t known anyone who’s been a serious crime victim for more than a decade. As the two of us wander the leafy streets of Condesa, seeing other couples walking their dogs and local professionals emerging from flashy bars to walk for blocks without a care at midnight, we feel downright silly for ever succumbing to the fear.

After a week of hailing taxis on the street and strolling through neighborhoods hand in hand with my wife, I’m realizing this city is probably safer than the one I live in myself. Apparently the statistics bear this out. Although Mexico City was once a poster child for urban chaos, it now has a homicide rate on par with Albuquerque, N.M.

Pollution is down, too, thanks to concerted efforts to move the worst offending factories, to limit which days vehicles can be on the street and to install cleaner bus systems. As we walk down the main boulevard, Paseo de la Reforma, on a Sunday, hundreds of people are riding bicycles on the closed-off street. The sense we get now is a city full of life and passion, one that plays a key role in the world economy and is a prime destination for foodies and art lovers.

Our intro to the big picture is the National Museum of Anthropology (Paseo de la Reforma in Chapultepec Park, tel 52 55 4040 5300, www.mna.inah.gob.mx; $5 admission). Hands-down one of the best museums in Latin America, if not the best, it is a visual delight on every level. Built by architect Pedro Ramírez Vázquez, the display areas form a U shape around a giant pedestal fountain and pools filled with turtles. The first floor focuses on pre-Columbian history in what is now Mexico, from the Olmecs and Toltecs through the Aztec and Maya civilizations. It is an amazing 20-acre collection, all presented with drama and flair. The second level is dedicated to the various indigenous tribes of the country, with costumes, sample kitchens, masks and videos of traditional dance performances.

Many of the main attractions outside of the center are spread out in different areas, with lots of traffic in between. Hiring a driver is one way to get to them, but we book excursions with Olympus Tours (Eridano 74, Coyoacán, tel 52 55 5684 8921, www .olympus-tours.com) in order to have some company and a good bilingual guide. These tours are reasonably priced and tend to over-deliver, with the itinerary grouping several highlights into one day. Our tour that ends up in the canals of Xochimilco, for example, first goes by the city’s World Trade Center with its dramatic public artwork, including a painted tribute to Mexico’s great muralists like Diego Rivera and José Clemente Orozco. Then it’s on to the city’s main bullfighting stadium.

Fittingly, we then visit one of the homes shared by Rivera and Frida Kahlo, the Blue House in Coyoacán. Not much of her work is displayed here. Dedicated fans should make their way to the Dolores Olmedo Patiño Museum (Av. México 5843, Xochimilco, tel 52 55 5555 0891, www.museodoloresolmedo.org.mx), which has a whole room of her paintings. The Blue House is more of a look into her life and where she spent much of her time, the kitchen set up much like it was when she ate here every day. The shady garden space outside pays homage to Mexico’s pre-Columbian past.

The nearby plaza in Coyoacán is the kind of place where we arrive and wish we could linger longer. Many who visit here on a short tour end up coming back another day to spend a lazy afternoon at a sidewalk café surrounding the park.

The city’s best-known attraction, the great pyramids of Teotihuacan, are well outside the metro area. Tours usually stop first at the Plaza of Three Cultures, containing the remains of ancient pyramids and a grand church built from one that was dismantled. Then they make their way to the Shrine of the Virgin of Guadalupe. The latter has far more appeal to devout locals than foreigners, but it’s an interesting display of Mexico City’s architectural challenges: All the older buildings surrounding the modern shrine are slanted and sinking, some dramatically.

We leave one day free for aimless wandering in the historic center, soaking up the ambience and hitting some of the highlights. First, the Palacio de Bellas Artes (Avenida Juárez and Eje Lázaro Cárdenas, http://www.bellasartes.gob.mx) opera house and museum by Alameda Park and the gilded main post office across from it. Then we get our art fix for free from two buildings filled with Diego Rivera murals: the Palacio Nacional on the main square and the Ministry of Education building (Argentina 28, Centro Histórico, http://www.sep.gob.mx) a couple of blocks away.

Surprisingly, the high point ends up being something that barely rates a mention in most guidebooks. At a small desk to the right of the entrance of the grand cathedral on the Zócalo, you can sign up to tour the bell towers. The two towers are situated on opposite sides of the roof, so in going from one tower to the other to see the bells in action, we walk across the actual roof of the cathedral, with a panoramic view of the bustling scene below and the seemingly never-ending city spread out before us. It’s a strange sensation and yet another quirky surprise in a scrappy city that keeps defying expectations.