Oaxaca city is small and the valley around it is not, and almost everything is a half or full day out.
Monte Albán, twenty minutes up a hill, is a Zapotec capital built on a mountain top that was levelled to take it — occupied for thirteen centuries, abandoned around 850 AD, and still one of the great archaeological sites of the Americas. Go early; there is no shade.
The valley circuit strings together the Tule tree at Santa María (the thickest trunk of any tree on earth), the weaving village of Teotitlán del Valle, the stone-mosaic palaces of Mitla, and the petrified waterfall at Hierve el Agua — mineral springs that have left calcified cascades down a cliff, with pools at the top. Hierve el Agua is on communal land and has been closed by the community more than once in disputes over who collects the entrance money; check it is open the week you go.
Mezcal is the other reason people come. The palenques around Santiago Matatlán distil in clay or copper from agave roasted in an earth pit, and a visit to a family palenque is a different experience from a tasting room in town — you see the pit, the horse-drawn tahona and the still. Any agency here sells the trip.
In the city itself: the Mercado 20 de Noviembre and its smoke-filled meat corridor, the Santo Domingo cultural centre and its ethnobotanical garden, and the food. Oaxaca is the best eating in Mexico and most of it costs very little.