Unfortunately I must also echo the concerns about crime in Mexico City. My mother-in-law was jacked in a cab last month, mid-day on a busy street in the city of Tlalnepantla (a suburb of Mexico City), by a couple of gun-wielding thugs. Fortunately she was not physically hurt.
Now for some more pleasant thoughts!
A nice outing is a visit to the town of Tepotzotlan just north of Mexico City on federal toll highway 57D. Tepotzotlan is a town which has as a highlight the church of Saint Francisco Javier, known for its stunning gold plated altars and religious art. The facade is decorated with a couple hundred sculptures of saints, angels, etc. The site is one of the most important locations of religious art in Mexico. The church and adjoining monestary are a museum. In front of the church is a zocalo (town square) around which you'll find plenty of family-run restaurants where you can enjoy a good meal and watch town life go by. Tepotzotlan is a favorite weekend destination for many people from Mexico City who go just to browse the shops and enjoy lunch on the zocalo.
For a slice of middle class Mexican life you might consider a visit a modern shopping mall. Well, La Cochinita always does when she goes home to Mexico City. One of the biggest and best is Centro Comercial Santa Fe, located west of Mexico City along the Mexico-Toluca highway.
One of my favorite restaurants in Mexico City is "El Cardenal"
www.elcardenal.com.mx They have a couple of locations, both in the Centro Historico district (in and around the Zona Rosa). I'm partial to the one at the Hotel Sheraton on Avenida Juarez because of the convenient valet parking, but I've also eaten in the one at Palma #23 (between the streets of Madero and 5 de Mayo). Everything is made from scratch at the restaurants and they have their own bakery and chocolate factory. Go for the traditional Mexican breakfasts!