The Santorini center is around the area of Nea Kameni Volcano and 1 mile east of Palea Volcano.
The current island of Santorini is what remains after an enormous volcanic eruption that destroyed the earliest settlements on the former island and created the caldera. My whole time in Santorini was spent in the capital city of Fira. The city literally clings to a cliff overlooking a lagoon. The bus ride from the ferry port to the city center was the windiest, steepest, scariest ride of my life, but the views overlooking it were the best I've ever seen. Fira is full of shops and restaurants and luxurious apartment rentals overlooking the Aegean Sea. The highlight of my day in Santorini was getting a pedicure by fish that nibble the dead skin off of your feet!
Below are reviews of the city of Santorini, Greece from an actual visitor's perspective.
You need to see Santorini 100%. It is beautiful and really a wonder of the world. The way the city is built on top of what is essentially mountain side is breathtaking.
The views, winery, ATVs, restaurants and shopping!