In Mexico, a dollar goes a long way. Cough up $20 and you’ll be thoroughly entertained, by anything from a professional wrestling match to a night of dancing to Latin music. And many of these options will steer you clear of the ready-made, foreigner-friendly Mexico, while you save money and live it up with the locals. Start with a free, self-guided walking tour in the Historic Center of Mexico City, where you’ll be impressed by the scale of the huge central plaza, the Zocalo.

If you go on a weekend evening, you may run into an outdoor concert, and during the day you’ll find street protesters, crafts vendors and traditional dance groups. The buildings surrounding the square date back to the Aztecs, whose ceremonial center was there before the Europeans built over it. At the Templo Mayor, just off the plaza’s northeast corner, archaeologists continue to excavate ruins of the civilization that fell to the Spaniards.

You can tour both the museum and the archaeological site for $4. Right next to the Aztec ruins is the city’s Metropolitan Cathedral, designed by 16 architects and built during two centuries. To the east is the National Palace, where stunning murals by Diego Rivera lay out the entire sweep of Mexican history. It’s free to enter, but well worth finding a free, accredited guide to the left as you enter or paying about $9 to one of the guides outside to explain the images.

As for Mexican music, there are plenty of options — swaying with a partner to romantic Norteno cowboy music and getting serenaded by a mariachi band. One of the best places to hear the costumed, guitar-playing mariachis is Plaza Garibaldi, where they ramble across the plaza and take requests from customers in the many surrounding bars.