The Old Port
Despite the long climb (or I suppose you COULD take the cable car or donkey) the old port is worth a visit. It's a hive of activity at most times of the day, especially so when there are a lot of cruise ships in. The ships can't dock at the harbour and everything and everyone has to be taken to/from them by launch. These boats are constantly on the move, and the various ships have embarkation stations set up on the harbour from where their passengers depart for their ships. These intermingle with the various day excursion departures which run fequently to the volcano, Thirissia and Oia.
As well as all the maritime activity there are a few tavernas and cafes down there, as well as a small church. There's also some kind of castle (old? new? I don't have any idea, but it looks more residential these days) built into the rock face. It even has a gun (definitely modern) mounted on a platform cut into the cliff. There are also a couple of colourfully painted dwellings which are also cut into the cliff side.

the nuns of Fira surviving the earthquake
Ursula and Ali
Riding up on the cable car
Virtual attendee Pieter checks out the menu