Well in august the islands (especially the Cyclades) are very busy but if you like that you can go for the classical but always lovely Santorini.

Finding an hotel in Imerovigli will allow you a little more quietness and amazing view on the caldera.

You are 5 mn away from Fira (the capital) and Oia, the 2 busy and nice villages of the island.

Look at those sites to start dreaming (dream has a price, the hotels in Imerovigli are pricey especially in this busy period)

http://www.santorini-hotels.info/santorini-island-map-hotels/hotels-in-I...

http://imerovigli-palace.com/

Personally I will not go to Santorini in August because I like deserted beaches and more green islands but if it is your first time in Greece and you like relaxing at the pool and busy villages it is a safe choice.