Breakfasts in Mexico are a lot more interesting than eggs and toast. Start with a cafe de olla (coffee made in a clay pot with brown sugar and cinnamon) or hot chocolate with bread to dunk in it, then move on to the main course. A lot of the popular Mexican breakfast dishes are tortilla-based. These chilaquiles are made with crispy fried tortillas that are drowned in spicy tomato sauce and topped with queso fresco, onion and parsley. A breakfast like this will give you plenty of energy for a day of sightseeing.
The markets in Oaxaca offer great breakfast options, especially if you're looking for a large meal that will fill you up and keep you satisfied until the late lunch that is customary in Mexico. The Mercado de la Merced has a few good options, including Fonda Florecita and Fonda Rosita, which both offer delicious breakfasts.