About any location will give the jaw dropping gorgeous sites. In many it is more shopping and eating than sightseeing. We spent part of the day in Oia which is reachable via public bus (30 mins) from Fira which is where the ship docks. Oia is more relax and prettier than Fira. Skip the mules. Around the corner from the top of the cable car you will find a number of travel agencies. Half day bus trips are available to some of the digs. On our next trip we will do that.
Small warning -- don't drink much. Bathrooms are a premium. We had a lovely lunch, big beer and expected to use their restroom prior to leaving. Doors locked. The staff's comments was, "No water." Had to get real creative after that. Also time your departure. The line for the cable car can become very long with rush back to the ship.