Well, the entire city is a place you need to be careful :) Although the violent crime rate has dropped a lot within last decades, petty crime is still a huge issue. I took a spare wallet and an old phone just in case, but once you learn the ropes (and don't behave too much like what Mexicans call a "gringo") you're quite safe.
I am glad you liked the post :)
Haha, yes, I know gringos very well. I'm definitely one of those, but I try not to stick out too much! I can at least pronounce some of the things unlike others in my family. I usually take a slim wallet when I travel. Something I can keep in my front pocket versus my back pocket.
Take a fanny pack instead, and wear it over your shoulder to fit among the locals ;)
I'm shocked that cross body bag trend hasn't run its course yet. I just can't bring myself to jump on that bandwagon!