In Oaxaca de Juárez I recommend El Llano over the Zócalo because, although it does have a church like all squares, it is not a religious, government, ceremonial, or tourist square, but a working square. It is so large I wonder whether it was one one of those enormous pre-Hispanic markets. I should find out.
The air in El Llano has wi-fi, and the present post was written on that after I visited the international news stand. I had just eaten a quesadilla of Oaxaca cheese and squash flower, with the tortilla made right before my eyes, from a food stall on the square. I had drunk orange water and was now sipping cactus ice.
El Llano has a lovely fountain, shoe shine men, stores with useful items in them, a bank with an ATM machine, a cultural center, several decent and inexpensive restaurants, two youth hostels, a nice hotel, and importantly, a theatre that has concerts on Fridays, as well as other events and a café; concert tickets are 50 pesos or about $4.50. At night, people jog around the square.
Down on Alcalá the one place not to miss is the Grañén-Porrúa bookstore, which has a wonderful selection of records as well. There is a café in the patio, and high quality arts and crafts are sold next door. The book selection is not as large as that of some of the best Mexico City stores, but it is easily as good and as I say, the CDs are fantastic — although this store does not also stock vinyl as the Péndulo (in the DF) does.