The centro neighborhood has a bad reputation, due to the fact that there was a white flight during the seventies, and a lot of destruction followed by further abandonment in the eighties. But during the past 10 years the city’s administration has invested millions in remodeling the city centre, not least because Mexico’s most famous billionaire, Carlos Slim, is buying a lot of real estate there, planning to make it as luxury and elegant as Manhattan.
So today statistics show that you have as many chances getting mugged in la Roma, Condesa or Polanco as in the Centro Historico. The idea that the city centre is dangerous stays atriums as an Urban legend however, which hopefully will slow down the gentrification process a bit .
If you are planning to visit Mexico City, and you are looking for a bit more then nice coffee shops and generic restaurants (which line the streets in la Roma and Condesa by now) , consider that historically, architectonically and in terms of culture the historic centre of Mexico City is undoubtedly the most interesting part of the city.