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I live and work in Mexico City. While there is always some degree of risk in any big city, I would not be overly concerned here if you use reasonable precautions. I have used my 5D3 downtown (Zocalo, Palacio de Bellas Artes), in the Chapultepec Park area, and other areas throughout the city.
Just use common sense. For example:
- Be discrete with your equipment (don't open a backpack full of cameras and lenses in the middle of a crowded market).
- If you need a taxi, have the hotel call one for you or use an established "sitio" (obvious taxi stand on the street with taxis lined up and possibly a little stand or phone). Hailing a random cab off the street elevates the risk of assault somewhat. The hotels often have "tourist taxis". They are usually larger autos and they are much more expensive but they can be worth it for an occasional visitor. Tourist taxi drivers are commonly bi-lingual, more chatty, willing to make trip suggestions, and more amenable to custom trips with multiple stops. It is usually possible to negotiate rate reductions for half-day and full-day excursions.
- Use a little more care at night, particularly in less-transited areas.
- I am always careful about leaving gear in hotel rooms, even for very nice hotels. I will put it in the room safe if the room has one and the equipment fits. If not, I will either take it with me or leave it with hotel staff in reception. Theft, in general, is probably the greatest risk so don't leave a bag or piece of equipment out of your site or control while out in public. Also, if you forget something (a lens cap, a lens left on a ledge after a lens change, etc.), don't expect to come back later and find it.
Mexico City has tons of photo opportunities of both the cliche/touristy and the normal/not-so-normal street-life variety. I wish you the best during your stay.
I'll let someone else give you current tips regarding Sao Paulo. It has been several years since I have visited there. I would suspect, however, that you should use a little more care there in downtown Sao Paulo and also if you decide to make a side-trip to Rio.