https://santorinisecrets.com/where-to-stay-santorini/ This is a great guide to the best places areas of the island to stay for whatever your budget or ideal type of vacation is. There are quite a few Airbnbs on the island too, which are always a great option. Here is a great video on the topic also: https://youtu.be/cwBr5fluKQ8?si=8m9SR3nb4v0VGuUq
https://santorinisecrets.com/santorini-bus-schedule/ Santorini’s local buses are called “KTEL Buses” or just simply Ktel Santorini and they operate all months of the year. The local buses of Santorini are the best and cheapest way to get around the island but if you really want to explore the island with much more flexibility you should rent a car or a quad.
It is recommended to rent a car, ATV or moped on the island. Here is a video explaining driving and parking on the island https://www.youtube.com/watch?v=f_LY6vt8s4o