Get to Matera quickly, because it’s still relatively undiscovered by foreign tourists. In town, visit the Domenico Ridola National Museum. Matera’s real claim to fame, though, and the reason it’s a UNESCO World Heritage Site, is the extensive series of cave dwellings ("i sassi") southeast of town, first inhabited by Benedictine and Basilian monks. You’ll see individual cells, chapels, and even some churches, many adorned with Byzantine decorations and frescoes.