I wear an old pair of Penney's work jeans with the hammer loop, and it is as if I am invisible. With gray wash pants, I am aggressively confronted on every block. Flashy cosmetics, jewelry, Calvin Klein jeans, and so forth, will make you much more visible and much more a target of panhandlers and crooks. I also recommend for maximum safety, for first time tourists, do not go out much at night. If you want night life, go to Acapulco or Cancun, with their discos and clubs.
Big cities are inherently more dangerous at night, period.
If you do choose to go out at night, watch the streets. When pedestrian traffic on the streeet begins to drop, it is time for you to go in, too. Amado Nervo, a street a block from my house, is filled with old women, women with kids, and children all day. After 10 pm, when the stores close, that street is empty, a sign of sure danger in a city where people do not go to sleep until midnight. Final tip - if you encounter someone who tries to tell you what a terrible jungle of crime Mexico City is, aggressively ask them several questions, and tolerate no 'blown smoke'.