Base yourself near the Zócalo, walk everywhere, and accept that you will never leave Oaxaca thin. The city's relationship with food is total — the mercados, the street carts, the fine-dining restaurants, and the cooking schools all draw from the same deep well. Take a cooking class on day two; it will make the rest of your meals richer.
The seven moles
Oaxaca is known as the Land of the Seven Moles, and if you eat carefully you can taste most of them in a week. Mole negro, the most famous, is a 30-ingredient sauce that takes two days to make. Mole coloradito, mole verde, mole amarillo and chichilo round out the core five; manchamanteles and mole rojo complete the seven. Do not rank them; each is a different idea of what mole can be.
Mezcal, properly
Mezcal is to Oaxaca what Champagne is to Champagne — a protected regional spirit with dozens of small producers, each working a different variety of agave. Do a distillery tour in Santiago Matatlán, taste everything neat, and never put lime or salt in anything you are served. The good stuff is a sipping spirit, not a shot.
Beyond the city
Rent a car for two days and drive the Sierra Norte — an indigenous eco-tourism network of eight mountain villages that have, between them, built some of the best sustainable tourism in the Americas. Cabins, trails, local food, and a view of the stars you will not forget.