One of the popular things to do on Santorini is walk the approximately nine-kilometer path from Fira to Oia. For almost all the way, the path is separate from the road and follows the cliffs facing the caldera.
We took the bus to Fira and then walked back to Oia. Early on, the path is paved and runs through the towns of Firostefani and Imerovigli. Once past there, it turns more into a gravel (and at times, small stone) path. There are uphill and downhill parts regardless of whether you are walking Fira-Oia or Oia-Fira, but Fira-Oia is generally more of a downhill walk than the reverse.
In total, the walk took about three hours, with plenty of stops for photos. There's little shade--pack sunscreen and lots of water!