From the bus terminal in Fira you can take a bus to Oia. The journey takes about 30 minutes and costs just € 1.60 per person (one way). You can purchase your ticket on the bus. The final stop in Oia is within walking distance from the center. You park even closer to the city center than the tour buses of the cruise lines. It's good to check the bus timetable in advance.
How do I get to the bus terminal from the cruise port in Fira?
First go from the cruise port to the center of Fira. Then turn right and follow the Golden Street, the main shopping street of town. The center is also indicated. When you see the Cathedral on your left, continue a little further. Just past the Cathedral turn left. The road goes down now. Cross the intersection and a little further to the left you can see the bus terminal. This walk only takes 10 minutes.