Hello mate,
this island is perfect for relax in many places, there are many beaches, many resorts, many other kinda stuff.
I was there several times, I live in Brindisi (where you can find cheap ferries to reach corfu…) and I can suggest many places.
If you like sand you can go to the north in Kassiopi. Nice and quiet place.
More groove and fun there is on the Eastern side on Ipsos (there you can find more english people than London) or Gouvia. In just few kilometers northern from Ipsos there is the gorgeous Barbati Beach. Blue sea with crystal water.
In the west side Paleokastritsa and Pelekas. Cold sea water, lot of fun.
But if you want some serious relax otu from tourist rails go to the south or the Kasiopi. Feel free to mail me anytime I can help you more.

Ciao,
Stefano