Am currently here at the moment. It's quite pleasant. I've been all around town with a Leica M6 with no worries about being mugged. That said, like being in all big cities mind your surroundings. But I've managed to walk around town camera in hand no worries. I have of course put it in my bag to take the metro, and have kept my possessions quite close to me and bag zips away from floating hands.
As for places to see:
Go see the courtyards of the stately homes in the centre of the city, like in the Colegio de San Idelfonso. Go see Coyoacan or San Angel, it's like a charming little towns within the city. Have a look around the university (UNAM). Go for a walk at the Alameda central.
For food, well if you like places with big ambience go to the Colonia Condesa and have a walk around. Full of restaurants catering to whatever you desire. Some personal favourites that are not so touristy:
Don Asado in Michoacan street in Condesa. Great Uruguayan meat.
La casa de Toño. In Narvarte on Cuauhtemoc near the Centro Medico metro. Super cheap and very tasty Mexican food. You definitely need to try the Pozole. Although mind the massive queues!
You can also try going to the Bisquets, Bisquets de Obregón. It's a chain of Mexican food restaurants, but they are worth a try anyway.
That's all I have for now. What else are you interested in seeing, or doing?