We had a blast in Mexico City last January. I totally recommend. We rented an AirBnB in the Condesa area and found it really nice - lots of beautiful architecture, pretty quiet, close to the metro, and good food nearby.
We were there for about a week, but we did a lot of day trips out during that time to explore other parts of central Mexico - one full day in Puebla and Cholula, a day in Teotihuacan, and a really fun tour on our last day I organized myself, by hiring a local driver and his son (to translate for us) and heading WAY out to Pachuca, an old silver mine, a bunch Pueblos Magicos, and the amazing Prismas Basalticos. If I was there again, I would hire the same guys and head out to some hot springs, but we ran out of time this trip. I think three days is fine if you're going to just stay within the city.
Definitely DO NOT miss going to a Lucha Libre show if you're there. We met up with some travelling redditors for a New Years Day special show, and our front row tickets to that gave us one of our best experiences in travel period, over all the years and countries.
Food-wise, I really preferred the street food to restaurants. It was absolutely delicious, and very cheap.
Cost-wise, looking at Mint it looks like we spent roughly $80/day for everything that wasn't flights or accommodation - food, activities, transportation, entrance fees, etc. We took public transit, which was pretty good compared to a lot of places, but also sometimes utter chaos with lots of signs that direct you to dead ends. If you've taken public transit in foreign countries a few times it shouldn't be a problem - we always eventually ended up in the right place. When we were in the city itself versus on day trips, we mostly explored different areas, wandered into random galleries, churches, and museums, ate interesting things, and just generally explored. We also attended the new years eve public festivities, which was really fun.
I'm not a great person to talk about safety because it just doesn't occur to me to be scared unless there's a direct and immediate threat - like, if there was a person with a weapon coming after me or something. That never happened. My boyfriend said he wasn't ever scared either, and he's jumpier than me, so I guess it's fine?