MEXICO CITY • Move over, greasy tacos and tacky trinkets: Mexico City is home to a vast network of chic museums, top-notch restaurants and trendy nightclubs. There’s even an ice bar.

What’s more, the city remains one of the globe’s best budget stops.

With just a few pesos – preferably hidden deep inside one’s clothing in case of mugging – visitors can view world-renowned art inside centuries-old buildings, wander through Aztec ruins in the heart of the city, and sip tequila at rooftop bars where DJs spin the latest international beats.

And amid the chaos of its more than 20 million people, the Western Hemisphere’s largest city also has plenty of breathing space. And despite Mexico City’s reputation for crime, your personal safety can be greatly improved by taking a few precautions.

GETTING AROUND: Hop aboard the Turibus, a double-decker bus that give’s you a bird’s-eye view while taking you to all the top attractions for less than $12. For less than 20 cents, the subway can’t be beat and is relatively safe. During rush hour, women can head to the front for the all-female cars. If you want a taxi, make sure it is from an official stand called a “sitio.” (This will keep you from falling prey to criminals who pose as cabdrivers, take passengers to ATMs and force them to empty their accounts.)

MUST-SEES: With dozens of museums, you can easily overdose on art in this town. Topping the list are the awe-inspiring murals by Diego Rivera and other Mexican legends in the Palacio de Bellas Artes, which also has temporary contemporary exhibits and a stunning performance called the Ballet Folklorico showcasing the country’s traditional dances.

Then walk down Francisco Madero Street to the Zocalo, strolling past the colonial buildings – including a tile-covered 1596 count’s mansion. Today the home is a two-story coffee shop and drug store called Sanborns.

Off the Zocalo is the Palacio Nacional, or National Palace, where Rivera painted the entire history of Mexico on its walls. It’s free and English-speaking guides are on hand to explain the details of the intricate work. Behind the main courtyard, the cactus and maguey gardens are a great place to take a break. On the other side of the Zocalo is the Metropolitan Cathedral, the oldest in the Americas.

Behind the cathedral, the Centro Cultural de Espana, funded by the Spanish Embassy, has extensive contemporary art exhibits and a rooftop cafe with mouthwatering tapas, most for less than $5. On Thursday nights, top DJs spin their tunes.

PREHISPANIC RUINS: The city is teeming with ruins. Archaeologists are still finding the buried treasures under plazas and buildings. One of the best is the Templo Mayor, or Great Temple, a site squashed between businesses and government buildings off the Zocalo. Workers discovered the Aztec religious center in the mid-1970s. The Aztecs are believed to have built the temple in the 1300s. The ruins include a wall of stone skulls representing the human heads the Aztecs used to put on display after sacrificing people to the gods. The entrance fee is less than $3. Better yet, on Sundays the museum is free. If you’re still craving more history, hit the National Museum of Anthropology in Chapultepec Park, one of the world’s best. Its entrance fee is less than $4.

NEIGHBORHOODS: La Roma and La Condesa are hubs of hipness and worth a day of strolling, shopping at the boutiques, stopping for Chiapas-grown coffee and people-watching in one of the funky cafes, or checking out the many art galleries. Start at Galeria OMR off the Rio de Janeiro plaza and wander down Orizaba street to Alvaro Obregon.

Then head to Parque Mexico. Check this bilingual list of galleries: www.arte-mexi co.com/galeries.htm.

SURVIVING THE MADNESS: If you’re overwhelmed by the noise of honking cars and shouting vendors, find respite wandering through the 550-acre Chapultepec Park – and the sprawling zoo is free. Or visit the free Jardin Botanico, or Botanical Gardens, of Mexico’s National Autonomous University.

NIGHTLIFE: Mama Rumba in La Roma is a sure bet to boogie away the night. On Wednesdays and Thursdays, the $4 cover charge also includes free salsa lessons before 10 p.m. when the live Cuban band kicks in. Traditional cantinas throw in sizable appetizers, almost a meal in themselves, with $3 beers. Try the 1928 Cantina La Guadalupana in Coyoacan, where Diego Rivera and Frida Kahlo drank tequila.

For the cutting-edge side of Coyoacan visit La Bipolar. Owned by actor Diego Luna (“Y Tu Mama Tambien”), the bar offers marlin tostadas and walls covered in plastic crates. In Condesa, you can grab a ski jacket and cool down with your tequila-based drink on the ice-made love seats at the Icebar.

Lucha Libre, Mexico’s masked wresting spectacular, is a must for lovers of kitsch. On Tuesdays, hit the small, traditional Arena Coliseo for the best two-hour show $2.50 can buy, or go for the glitzy televised productions at Arena Mexico, where tickets run between $4 to $13.

BEYOND TACOS: There’s no better place than the capital to get a sampling of Mexico’s diverse food. La Tecla in La Roma is one of the most affordable places to try Nouveau Mexican food, such as duck enchiladas with mango sauce. Most meals are less than $10.

For amazing corn-flour tamales, try Flor de Lis in La Condesa. Two tamales cost less than $3.

If you want to spot a Mexican celebrity but stay on budget, stop by Frutos Prohibidos y Otros Placeres, an outdoor corner cafe with a long list of fresh-fruit smoothies, salads and wraps in La Condesa.

MARKETS: The Ciudadela market in the city’s center has the best prices and most variety for traditional crafts. It’s open every day. For more upscale art, try Bazaar Sabado on – you got it, Saturdays – in San Angel.

If you read Spanish, pick up Chilango or Donde Ir magazines for articles and reviews of the city’s happenings. If not, you can probably muddle through Tiempo Libre, which lists restaurants, movies, plays and other events.

tourists riding a double decker Turibus make their way though downtown Mexico City. Photo by (AP Photo/Gregory Bull, File)