Although I love Kamari beach, there are several beaches in Santorini and to give you an idea of some of the others, this is Perivolos (or little Perissa). It is much calmer in both wind and surf than Kamari, but also the atmosphere is quite different. Perivolos is very small and quiet with a total of five restaurants and one shop on the entire beach. You may prefer this if you like quiet beaches with amenities and don't mind paying $100 for a Tshirt (the price in the one shop on the beach).
There is also sand here as opposed to the rocks and pebbles of Kamari.
Akrotiri on the Southern end of the island is a very barren secluded area, with only one hotel and attached restaurant/cafe.
If you walk around the bend here you will arrive at the famous Red Beach and Moon Beach.
As you walk around the bend, you see sights like this, where the sea and surf has literally washed away what used to be homes and restaurants (although a few restaurants still remain and are operational).
Climbing to the top of the hill to Red and Moon beach, there is a church built into the hillside.
To get to Red and Moon Beach, you must climb over the hill, like these people.
Or climb past the boulders like these people to get the the Red Beach that looks like it is on Mars.
To get to Moon Beach, you must climb over the hill to the white part showing on the left part of the photo.
This is Moon Beach, which is even more barren and secluded than Red Beach.
I chose to just take pictures and hiked back to the hotel in Akrotiri to sip a freshly squeezed orange juice as I watched the waves.