But if you are looking for a less typical beach go somewhere else, away from the well-known destination beaches and the crowds they attract. The best swimming on the island is below Oia at the end of the seawall that begins on the wharf in Amoudi Bay. There's no beach but there are large rocks and a man-made platform down there for sunbathing. This is what it looks like: http://tinyurl.com/kwnqvo3
Vlichada Beach is another interesting one and it's less-crowded than Kamari and Perissa: http://tinyurl.com/mprpjqf
From Vlichada you can take a water taxi to White Beach, but don't go to Red Beach as it's very dangerous. The rock cliff above the beach is extremely unstable and large boulders can fall onto sunbathers without warning.
Perissa and ...Vlichada Beach.
you can do a day trip to ios island too ,they have the most amazing beaches and coves , a lot of the locals pop over to ios too
Perissa - If for general swimming, less crowded as its more spread out and the chance to eat at the wonderful Ntomatini.
Kamari - If you fancy swimmimg out to the two large clusters of boulders in the water. Then finish the day by walking to the open air cinema on the outskirts of the village. Movies are in English (with Greek subtitles) and start at 21.30.
If you want to be active - start at Perissa early and hike up to Ancient Thera (opens 08.00-15.00. Closed Mondays). Walk down to Kamari.
Otherwise, there's a water taxi between the two resorts between around 10.00-17.30 (doesn't operate in high winds). You'll need to wade a little into the walk to board / disembark the boat.
Out of the two it would definitely be Perissa for me due to the much longer and less crowded beach.