The Centro Historico (Historic Center) is one of few places in the world where you feel the weight of many centuries of civilizations layered on top of each other. The massive Zocolo sprawls out in front of the Mexico City Metropolitan Cathedral, one of the first major (de)construction projects undertaken by the Spanish colonists. Just behind that are the ruins of the Templo Mayor, the premier Aztec religious and political site that the Spanish destroyed to build their cathedral.

The Frida Kahlo Museum—housed in the artist’s “Casa Azul,” or Blue House—is at the top of many travelers’ must-visit lists, so make sure to pre-book tickets. But you should also consider seeing two other museums related to Frida and her lover, Diego Rivera. Start with the Diego Rivera and Frida Kahlo Studio-Museum, which is less busy than the Casa Azul, and located in a fascinating pair of buildings designed by the couple’s friend Juan O’Gorman.

Markets are a way of life in Mexico City and new visitors should head to the Mercado de Coyoacán, a relaxed space near the Frida Kahlo Museum, where you can try tropical fruits and fresh quesadillas. If you’re somewhat market savvy, head to La Merced Market, a bustling center of commerce near the Historic Center. Market experts should opt for the magnificent Central de Abastos, which covers nearly the entire Iztapalapa borough, far from the center.

The ancient city of Teotihuacan, technically situated in the neighboring State of Mexico, is largely a mystery to archeologists. In fact, even the name itself comes from the Aztec language, as we don’t know what the inhabitants of the ancient civilization who once lived there called themselves. The pyramids at Zona Arqueológica de Teotihuacán are a reminder of the centuries of complex civilization that existed in the Valley of Mexico before colonialism.

Youth culture is going strong in Mexico City, and there are bars and hangouts for every subculture you can imagine, from punks to metalheads to bookworms. Get your feet wet with a concert at 316centro, which often features experimental local acts. Alternatively, check out the headquarters of Radio Nopal, an independent radio station that spotlights local talent and is a hangout for musicians and DJs.

Visit the nearly century-old Salon Los Angeles, near the historic Plaza de Tres Culturas and the massive Tlatelolco housing development (just be aware that the dance hall is only open Tuesdays and Sundays). For those less inclined to show off their moves, try a traditional pulqueria, where the pre-Hispanic drink pulque is the star of the show. Alternatively, opt for a traditional cantina, such as Los Cuates, where multiple courses of food are included for free with a minimum order of drinks.

The National Museum of Anthropology is one of the best and largest of its kind in the world. You really can spend a whole day here; while most visitors head straight for the Aztec room, take your time with the incredible artifacts of cultures whose names you may not even know, or explore it on a cultural tour. Make sure to explore the upstairs level (which many visitors tend to skip). It focuses on the ethnography of the Indigenous peoples who call the region home.

The home to one of the world’s largest universities, the National Autonomous University of Mexico (UNAM), University City really does feel like a city all in itself. There’s plenty to do here, shoulder-to-shoulder with thousands of students. Visit the University Museum of Contemporary Art (MUAC) or walk through the concrete Espacio Escultórico. Tour the colorful mosaic murals decorating the Central Library and other major buildings that inspire the pursuit of knowledge.

As much as food markets define the city and the ecosystems that drive it, another type of market is a key Mexico City attraction you shouldn't miss. The rough-and-tumble Lagunilla Market on Sundays is a wonderland of antiques, rarities, and curiosities. Not everything you see is as it’s marketed, but that’s part of the fun: digging through fakes to find the one gem that makes the trip worthwhile. Even if you aren’t as interested in clothes or antiques, you can enjoy ordering a massive michelada.

Mexico City is massive in so many ways, but even a lot of locals don’t know that there’s a volcano within the boundaries of the city itself. Ajusco is no small peak, either. It stands at 12,894 feet (3,930 meters), well above where many people start feeling the effects of high altitude. It’s a serious climb, but the reward makes the exertion (and lack of oxygen) worth it. From the peak, you should be able to catch a great view of the expansive metropolis stretching below you.