We went the other way around, that is from Oia to Fira, because we wanted to go from our first hotel at Oia to our next one at Firostefani by hiking. The trail was easy to find from Oia but beware, it is slightly uphill going that direction therefore more tiring and longer to finish it. Also, the view is better the other way around since its descending. Our GPS showed something over 9km and it took me and my fiance almost 4 hours to do it with 5-6 breaks to rest and look at the view.
The view is spectacular and worthwhile the effort! We saw some of the best located hotels along the way, perfect for isolation and relaxation. I wish I knew it before to stay one night there! This hike made for the best day on the island. Tip: if you plan on doing it at the end of the season, bring along a coat, it blows a lot when on top.