Yes its easy to get around by bus
Santorini is not known for its beaches (try Naxos for far better). They are, like many beaches in Greece, rocks instead of sand (bring water shoes, in case you don't know about that already. Its painful to walk on the beaches). Red beach is supposed to be good and has the benefit of being right next to the Akrotiri archeological ruins (not castle - two separate akrotiri's), which my teens really liked. We splurged and took a sunset cruise on a catamaran, where they feed you dinner and take you around the caldera. It lasted 5 hours. My kids enjoyed that. I liked it for about 3 hours ;) (Not really our thing so there's that).
As for lodging, we found it hardAirbnb, or whatever site you prefer) for a house or apartment rental. Thats usually the way we travel for this reason, but as I say, especially throughout Greece we stayed in two rooms when we stayed in a hotel or b&b