During fiestas, snack stalls along Hidalgo at the cathedral-front Alameda de León square abound in local delicacies. Choices include tlayudas, giant crisp tortillas loaded with avocado, tomato, onions, and cheese; and empanadas de amarillo, huge tacos stuffed with cheese and red salsa. For dessert, have a buñuelo, a crunchy, honey-soaked wheat tortilla.
At non-fiesta times, you can still fill up on the sizzling fare of taco, torta, hamburger, and hot dogs (eat ’em only when they are served hot) at stands that set up in the same vicinity.
For relatively economical local fare, go to the acre of food stalls inside the Mercado 20 de Noviembre, two blocks south of the zócalo’s southwest corner. Adventurous eaters will be in heaven among a wealth of succulent chiles rellenos; piquant moles (moh-LAYS); fat, banana leaf–wrapped tamales Oaxaqueños; and savory sopas (soups) and guisados (stews). Insist, however, that your selection be served hot.
Alternatively, take a look around the completely untouristed Sánchez Pasqua market (8 a.m.–2 p.m. daily except Sun.) for some pleasant surprises. (From the zócalo Cathedral, walk uphill along Garcia Vigil seven blocks to Humboldt and turn left a block to Porfirio Díaz. The market is past the gigantic laurel tree.) Enjoy the town’s tastiest comal (charcoal-fired griddle) cooking. Ask for Carmen Hernández Ramírez and order her memelas (big, thick, open-face tortillas smothered in beans, $1.50) and/or the luscious, plump tamales ($1.50) of Catalina Minerva Paz.
Much farther up the economic scale, sample the delicious offerings of 
Hostería Alcalá (Alcalá 307, 8:30 a.m.–11 p.m. daily, $5–15), four blocks north of the zócalo. The airy, tranquil patio ambience is ideal for a relaxing refreshment or lunch break from sightseeing along the Alcalá pedestrian mall.
For coffee and dessert, you have a number of additional downtown choices, notably Coffee Beans (Cinco de Mayo 400, cell tel. 951/162-7171, 8 a.m.–11 p.m. daily), five blocks north of the zócalo; or nearby Restaurant La Antigua (a block east at Reforma 401, tel. 951/516-5761, noon-11 p.m. daily, $3–8), just uphill from Abasolo.
For baked goods, a quartet of good carryout bakeries stand within a stone’s throw of the zócalo. First, try the sweet offerings of Tartamiel Pastelería Frances (on Trujano, half a block west from the southwest corner of the zócalo, tel. 951/516-7330, 7 a.m.–8 p.m. Mon.–Sat., 8:30 a.m.–7 p.m. Sun.). Continue clockwise, north of the zócalo a block, to Panadería Bamby (at the northwest corner of G. Vigil and Morelos, 6 a.m.–9 p.m. Mon.–Sat.).
A block east of the zócalo, stop by either the Pastelería and Café La Vasconia (Independencia 907 between Cinco de Mayo and Reforma, tel. 951/516-2677, 8 a.m.–9 p.m. daily, $2–6), with an inviting arched interior patio and a luscious selection of pastries, cakes, salads, and sandwiches. Another option is Pastelería Quemen (8 a.m.–9 p.m. daily), across the street.