I love going to museums, especially when I'm in a new city. I think it teaches you a lot about the local culture and vibe. Most of everyone that I asked for recs told me to check out the Anthropology Museum and it did not let down. It is housed in a really impressive building (pictured above) which in itself was worth checking out. Other things worth noting : the Mayan and Aztec exhibits were the most interesting and the outdoor area at the back of the museum was really well designed and a fun experience. This place was def worth a stop.
I haven't really been to many places in the world that let you experience and be surrounded by remains of ancient civilizations. That's why going to Teotihuacan, the site of the ancient Pyramid of the Sun and Moon, was a particularly special experience. I strongly recommend going here if you are in Mexico City - try to go early in the morning though, right when it opens (I think 8am). There is really no one there at this time and its really surreal walking around by yourself hearing the echo of your own foot steps. You cant help but think about how thousands of people came together to build these structures with no technology whatsoever and would live, worship and play here. Wild.
There is an incredible amount of fascinating history behind this place that you can read about on the wikipedia page.