Cafe de Tacuba
Housed in a former convent, this institution serves up tasty Mexican dishes all day for reasonable prices. It is very popular so arrive early. Menu is in English and Spanish.
Cafe La Opera
This restaurant has been serving Mexican food since the early 1900's and retains the same furniture since then. When you get there, look up to the ceiling, as you will see the famous gun shot accidentally fired by Pancho Villa.
Cafe el Popular
A quintessential breakfast joint offering a range of tasty egg dishes for well under US$4 and surrealistically low chrome ceilings.
Dulceria de Celaya
This confectionery shop sells old fashioned sweets. It was established in 1874 and still has its original cabinets from that age.
Ostioneria Las Palmas
Fantastic ceviche, superior huachinango al ajillo; everything very fresh, very tasty and very inexpensive.
La Terraza
Restaurant on the roof of the Hotel Majestic overlooking the Zocalo. Stunning panoramic views of the city.
El Huequito
This taco joint is good if you wanna try Tacos al pastor, as featured in Anthony Bourdain's Mexico show.