Depending upon which way the wind is blowing, you should go to one of the beaches protected from the wind - opposite to the direction of the wind. The prevailing wind on Kythera is the westerly, and the eastern and southern beaches are usually the best protected.
You can check the weather predictions on this great website:
http://www.meteo.gr/meteoplus/cf-En.cfm?city_id=19
St. Nikolaus
Platia Ammos
Limni (also known as Aphrodite's Beach)
Kaladi
Paliopoli
Avlemonas
Diakofti
Neos Kosmos
Firi Ammos North
Lagada
Halkos
Kapsali
Firi Ammos South
The Magic Green Pool
It's an hour's walk from Limnionas, and you need good shoes, but well worth it. See the pictures on the Sights page.
Kalami (you need to climb a bit)
Likothimo (not that pretty, but good when there is an easterly blowing