The UNESCO Site ruins are about 20 minutes outside of Oaxaca City. There are plenty of tours or you can get there via taxi for ~$250mxn. Per our favorite source (wikipedia), "Besides being one of the earliest cities of Mesoamerica, Monte Albán was important for nearly one thousand years as the pre-eminent Zapotec socio-political and economic center. "
"Located about 40 miles from Oaxaca, Hierve el Agua makes a great day trip from the city. Here, you'll see two waterfall-like rock formations which were formed when mineral-rich water spilled over the cliffs and trickled down the mountainside. At the top, you can take a dip in the man-made pools while enjoying awe-inspiring views. While they're not thermal springs, the waters were said to have healing properties due to their high mineral content. The easiest way to get here is via a private tour from Oaxaca. It's recommended to arrive early for thinner crowds. – Tripadvisor"
Take a walk through the oldest trading market in Oaxaca City and check out artisanal handicrafts and artworks, spices and food
Ornately designed historical cathedral located in the city center
"The Museo de las Culturas de Oaxaca is a regional culture museum that walks visitors chronologically from ancient times all the way to modern-day Oaxaca. Other halls are thematic, featuring Oaxacan medicine, music, language and pottery – and show that much of the cultural traditions have endured." The museum is open Tuesday- Sunday, from 10 am-8 pm, with the last entrance at 6:15 p.m. Admission costs ~70 mxn pesos (~$4usd).