Wonderful pictures of Ixta and Popo!
As a middle-aged woman traveler, I felt fine in DF, and I walked around during daylight hours in the area around the Zocalo, to Bellas Artes, to Plaza de Santo Domingo, on Reforma and around Chapultepec, and I took the metro in the regular cars (not the too-crowded women-only cars). Whether or not it was wise, I walked back around 11 PM from a performance at Bellas Artes to Hotel Catedral, probably about 5 or 6 blocks.
You can see signs of high security everywhere. The cash register is often behind glass. Many establishments have a security guard in front (although I think he is unarmed, so I'm not sure how much he can do).
A friend who is a resident of DF was car-jacked a few months ago at gunpoint, but I guess that happens in US cities too.
For the poster whose friends were robbed, sorry for asking specifics, but what weapons were they threatened with? What was the outcome? I know I was lucky, and I know I stick out from 1000 feet away as a gringa tourist.
The hotel clerk at Hotel Catedral marked the safe streets for me to walk, in the area of the Zocalo, on a map. I can't say how she would know that, but I took her word for it.
Although I know people have done it, I personally would have felt uncomfortable going to Mexico City if I didn't know at least a little Spanish. In most major European cities, if you start out a conversation haltingly in the local language, the service provider or whoever will take pity and respond in excellent English. Not so in Mexico City, for the most part.