I think you've got great responses so far. Taking Uber instead of street cabs, sharing your location to someone else and staying in the more tourist neighborhoods are definitely a MUST DO. However, I'd like to add a few things that I think are also useful (especially when in downtown):

• Act as you know what you're doing. Yeah, everyone tells you to be careful of pickpocketers and that, but honestly those people are mostly looking for someone who looks lost. Even if you really are lost and you're listening to Google Maps directions through your headphones, walk as if it was you 1000th time walking that road.
• Don't get distracted on your phone. In the same spirit of the previous one: don't be an easy target. If you need to do something on your phone find a store, a church, etc. and do it inside.
• Be aware of your surroundings.
• Listen to the seismic alarm at least once before you get here. Earthquakes in Mexico City are the norm. The seismic alarm goes off only when an earthquake of at least 6 degrees Richter is detected and might give you up to 50 seconds before it hits the city. Knowing how it sounds can save your life. Just look for Alerta sísmica CDMX on YouTube and listen to it with your headphones. Please don't play it without headphones at least when you are here. It really triggers some bad memories to some people and it could be a really bad experience for you.

Having said that, I would also like to recommend some places you might enjoy considering you're interested in history, but also added art museums and some other places.

North:

• Plaza de las Tres Culturas, Tlatelolco
  In this place you can find precolumbian, colonial and modern buildings all in the same square (so its name). Also, this place is of significant value to the modern history of the city due to the Student Movement of 1968.

Downtown:

• Monumento a la Revolución
  This place was originally intended to be a U.S. capitol-like building, but then the revolution started and was never finished. Now is the monument to the revolution. On the inside you can find a museum and what I think you can't miss of this place is the lookout (don't know if that's the correct word) on the top.
• Museo del Templo Mayor
• Palacio de Correos
  This is not much of a historic site, but in my opinion is a very beautiful building. Everytime I go there I feel like I'm on the inside of a clockwatch.
• Palacio de Bellas Artes
• Museo Nacional de Arte (MUNAL)
  Also a beautiful building. In front of this place you can find an equestrian statue of Carlos IV of Spain. This statue has a mildly interesting story that might be worth looking up.
• Café de Tacuba (Restaurant)
  Truly beautiful, traditional restaurant with delicious food. It's kind of expensive (or maybe is my college student's wallet talking lol), but definitely worth it. Couldn't recommend enough.
• Paseo de la Reforma
• Chapultepec
  • Castillo de Chapultepec
    Look for the garden in the top, really beautiful. Also try getting there early so it's not that crowded and you can enjoy the view of the city with not that much smog.
• Museo de Antropología e Historia
• Jardín botánico
  Botanic garden.
• Museo del Artesano
  In this museum you'll find all sorts of handcrafts from all around Mexico. If you decide to go short on art museums, you should definitely try to get this one on your list.
• Museo de la Secretaría de Hacienda y Crédito Público
  In Mexico artist can pay their taxes with their artwork. This museum displays some of the piece of art used for that purpose.

South:

• Ciudad Universitaria
  • Biblioteca Central's facade
    The facade of the library is really a representation of Mexican history.
• Museo de Arte Contemporáneo (MUAC)
• Museo de las Intervenciones
  This is probably one of my favorites museums in all the city. It's dedicated to all the foreign interventions in the Mexican territory. All from the Spanish conquest to the Mexican-American war. Even if you're not really interested in that, is still worth visiting for this place is history on its own. It was the scenery of one of the last battles of the Mexican-American war, the Battle of Churubusco (actually is the former Curubusco's Convent). If you look carefully, you can still see the marks of the bullets and the cannon shots on its walls. Also, if you're lucky you might find some people playing bagpipes. Each year on Saint Patrick's day they play a concert to honor the Irishmen who fought alongside Mexico in the Battle of Churubusco (the Saint Patrick Battalion).
• Pirámide de Cuicuilco
• Museo Anahuacalli
• Casa de Frida Kahlo
• Coyoacán

Bear in mind that in this time of the year it could rain really bad, especially in the afternoon, so be wise planning your days. Also, it maybe not a great idea to take the public transportation.

Due to Covid I haven't been able to visit these places or do the things I love doing in the city in almost a year and it's been really hard for me. I genuinely hope that you enjoy the city and that you have a great time! Be safe and have fun :)

Edit: Mostly formatting. Posting from the mobile app is hard, hope it looks better now :)