Mexico is a serious coffee-growing country — Chiapas and Veracruz in particular — though that quality doesn't always make it into Hotel Zone resort buffets, which often default to a generic drip blend.
Where to find the good stuff
Independent cafés downtown are the best bet for coffee that highlights Mexican-grown beans specifically, often roasted locally or regionally rather than imported. It's worth the short trip off the Hotel Zone strip if coffee quality matters to your trip.
What to order
Café de olla is a regional specialty worth trying at least once — coffee brewed with cinnamon and unrefined cane sugar (piloncillo), traditionally in a clay pot. It's sweeter and spiced compared to a standard black coffee.
Downtown café culture
Parque de las Palapas and the surrounding streets have a reasonable and growing café scene, useful as a slower-paced break between market browsing and lunch.