The Museum of Oltenia is the best place in Craiova to understand the wider region. Its collections are split across several buildings, covering history and archaeology, ethnography, and natural science rather than trying to squeeze Oltenia into one neat story.
The ethnography section is especially useful if your Romanian trip has been mostly cities so far. It gives a better sense of the rural crafts, pottery, clothing, and domestic life that shaped the plains and hills around Craiova.