I was in Mexico City last year for about a week. I have lived in LA, New York and now San Francisco. I never felt unsafe or threatened anywhere I went. I stayed on the well beaten tourist path for the most part. I walked all over the city at all times of the day and night. Took the subway quite a bit (it's really fast and cheap). Took a bunch of cabs (Dealt with maybe 1 greedy cab driver and he had the upper hand so I paid $6 for a $3 fare)

You will have no problems enjoying this wonderful city. The only area that looked sketchy to me was when I was leaving the airport, and that's not really a place a tourist would hang out.

One other piece of advice, English is not spoken as commonly in Mexico City as in other international destinations, (i.e. many of the museums do not have English translations available either) So I got lost a few times and did have a hard time finding someone who could give me directions in English. For some reason I always found the best English speakers working at Starbucks!

Enjoy