Greek Island Holiday?

For my summer holiday i'm hoping to go to a Greek Island. I'm also hoping to go somewhere where I can get by without the use of a car. Can anybody suggest anywhere this is possible?
Hoping to find somewhere where a beach, restaurants, shops etc are in easy reach. Thankyou.

Of course, as the rest of the answers indicate, too, there are many options... The following webpage which contains live webcam views from many Greek islands, travel videos and travel information, may help you decide which Greek island best fits your requirements as well as your personality:

http://www.livefromgreece.com/Live_Webca...

Good luck and happy travels!

Santorini is a great island to visit. You don't need a car, but can always get a donkey ride =)

have a great time!

Mykonos and Santorini..:) Have fun.

Mikonos And Santorini are the most tourist organised islands in Greece

ikaria a small island the god made the paradise there and is cheap near to samos....august is the best month for this island i spend 3 years now my holidays

Smaller islands - close to Athens
Spetses - No cars there!
Hydra
Poros
(you can also travel between the 3 easily by daily ferries)

Parga on the mainland (used to be a small fishing village)

Actually most resorts you visit will have your list on its doorstep - but with the larger islands you'll miss the rest of its beauty and what it has to offer. If you don't use a car I would strongly suggest public transport / water taxis

go to Rhodes.
Stay in Rhodes Town and you will have anything you want within walking range.
Shopping, bars, restaurants,beaches, historical monuments ( a lot)