Take it from a life-long postcard collecter and sender, the modest little show currently on the second floor of the Museo de la Ciudad de Mexico, in a colonial building in Centro Historico betweeen Pino Suarez and Zocalo stations, is a fascinating portal into the life of the metropolis, told through postcards. Apologies for the quality of the images as I'm using a standard Sony Cyber-shot (You can see my reflection in some of them), but here is a sample of some of the postcards on display.
The portrait postcards that give you that Gilded Age decadence feel are the trippiest. Other interesting ones celebrate the 1968 Mexico City Olympics in Modernist colors and lines, or idolize past national heroes and presidents. (The museum provides magnifying glasses to examine the cards more closely.)