Just need a list of things I cannot miss while I'm in the city. Will be staying in Santa Fe!
I know you only have 24 hours but I had made this 4-day itinerary for a friend this spring and thought I'd still share it. According to what you like to do, pick a day and do those activities!
Zócalo and El Centro Bolsero. Visit the Mexico City Metropolitan Cathedral which rests atop the old Aztec city and join the tour to see the top of the cathedral's bell towers or campanarios (if available when you go) http://www.mexicocity.gob.mx/detalle.php?id_pat=3908 You pay at the cathedral and there are set times and limits per tour. After seeing the cathedral and walking around Zocalo http://travel.nationalgeographic.com/travel/city-guides/mexico-city-walking-tour-3/ go to the Museo del Templo Mayor museum and see the Aztec ruins that have been unearthed and exist below the city. One of my favorite places to visit in Zocalo is the The House of Tiles, which is now a Sanborns and you can eat there, the local gold markets to buy jewelry- but be aware of pick pocket-ers- are in this area. Don't go with bags or flashy outfits that call attention. That will probably take you a day or if you're doing things quickly a half day to see this area, but don't rush yourselves, it is truly one of the most historic places in the city. After you're done touring have dinner nearby; if desired go to this very popular restaurant, El Balcon del Zocalo http://www.tripadvisor.com/Restaurant_Review-g150800-d1201096-Reviews-Balcon_del_Zocalo-Mexico_City_Central_Mexico_and_Gulf_Coast.html or head to your hotel to rest! There are also some up and coming and wicked cool parties in Zocalo buildings nowadays so if you want to dance in some eclectic house fashion check these parties out http://www.comunidadelectronica.tv/index2.html
La Villa-Basílica and Coyoacan. Wake up early and go see the largest basilica in Mexico and one of the largest in Latin America. You can get there in the metro, but again dress simply. http://www.metro.df.gob.mx/red/estacion.html?id=89 while you're there you can visit Juan Diego house, go atop the mountain where the first church for Virgen de Guadalupe was erected and get a great view of the city for photos, visit the local souvenir market that sets up below the basilica as well. There's not much else to do so once you're done head back to the metro and go to Coyoacan for lunch and more touring. Once in Coyoacan walk through the "city" center. Coyoacan is one of the oldest neighborhoods and was once the city's center. There are two mercados, the newest one sells everything from food to souvenirs and the oldest one sells mainly food so enjoy lunch there. The oldest one is next to the church in the center of Coyoacan. Also visit Frida Kahlo Museum, Palabra México Informando or the hundreds of shops around the center http://www.timeoutmexico.mx/df/arte-cultura/museos-en-coyoacan After, I highly suggest you grab dinner at Cantina La Coyoacana, it has a Mexican-style "beer" garden in the back, offers great food and is popular with young and old alike https://foursquare.com/v/la-coyoacana/4b9b0b70f964a52050ee35e3 It's one of my favorite spots there. After food and drinks head to your hotel to rest or go out-again!
Xochimilco. This will be a whole day affair and if you have more friends I highly suggest you all go together, get a trajinera (float) and take the "tour" of eating, getting a mariachi and cruising through the canals http://en.wikipedia.org/wiki/Xochimilco It's about an hour away from the city so I recommend you book a private taxi through your hotel there and back, don't take public cabs overall. If you'd like you could also take the metro there but I am not familiar with the route, Google it. There is a flower, food and souvenir market in the area as well so you will see lots and once you're done you can head to your hotel to rest. It's a thing you need to start by 10 a.m. at the latest because it gets busy and specially packed on weekends!
The National Museum of Anthropology and Paseo de la Reforma. There are a ton of things to do around Reforma but as you drive to the museum (which is HUGE and I don't think you'll want to see all of it) you will pass Ángel de la Independencia (our golden angel) and some of the ritzier areas of the city. I suggest the museum because it is one of the largest and most curated in the world so it's worth a visit, but again it is quite large and you really do need the whole day to see it. In case you just want to check it out head to the neighborhoods of Roma or Del Valle to see more hipster shops, eat good food, grab a drink and walk around. These two are the hot spots at the moment. And, again, there are other attractions you can check out: http://travel.nationalgeographic.com/travel/city-guides/mexico-city-must-dos/ or by area https://www.airbnb.es/locations/mexico-city
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I have a list of must in the city:
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If you have just one day then I would say head down to Coyoacan where you have the blue house where Frida Kalho and Diego Riviera used to live.
The house is very interesting to visit and Coyacan is one of the most pleasant parts of Mexico City with a nice bohemian vibe to it.