No matter which Greek Island(s) you choose, you are sure to find enjoyment and beauty including: sandy beaches, secluded coves, spectacular scenery, ancient and medieval sites, lively nightlife, peace and solitude or a just good dose of traditional Greek hospitality, cuisine, wines and atmosphere.
Of course some islands are more equal than others depending on your personal point of view, desires and budget so choose wisely. If you do have the time and the money then jump and the Greek island net shall appear! Either way you won't be sorry.
To me at least, Islands vary most in the amount of tourism received. This simple fact changes everything about an island. There are popular islands and those less so but for different reasons than you might expect. Some beautiful islands get very little tourism either because few know about them and they are undeveloped or hard to reach or both. They might also suffer from a lack of water and thus escape the developers machinations. This is true of many island beaches that are just screaming to be ruined by development but which, due to lack of abundant water or access are thankfully left alone. Oft times its worth packing a day kit and taking the local caique to remote beaches.
For some Greek island hopping suggestions this may be illuminating.
Geologically the Greek islands are mountain tops around which the sea has risen since the last ice age. Things warmed up, water melted, land bridges disappeared and islands formed. The Aegean lies at the conflux of three continents: Europe, Asia and Africa and there are many species of fauna, reptiles, amphibians, mammals and even birds common to all three. There are also many niche species that are not to be seen elsewhere because of the hindrance of the intervening sea. This barrier to colonization means that some species common to others areas of Greece and the 3 continents do not occur on some of the islands while others thrive. Miniature elephant remains have been discovered on several Greek islands so the land bridge was no myth.
If you are fortunate enough to be able to spend 2 to 3 weeks on the Greek Islands or even on just one Greek island, only then, will you really start to experience the decompression and lightening of soul that such an extended stay on a Greek Island will surely impart.
As your jet lag fades and one day blends into another your inner clock will adapt to a new heliocentric lifestyle freeing you of the hustle, bustle and regimentation of so-called modern civilization. Your most important daily decisions may be where to eat and what beach or bar to go to. You will still need money but the best things in life are almost free. Slowly but surely if you allow yourself to be exposed to them, the primeval rhythm of the pounding surf and the wonder of the star filled nights will cleanse your psyche. With care, and like your tan, these feelings of deep relaxation may last a few weeks after departure as well! People with pale complexions should be careful of sunburn and bring a sun hat and an extra large tee-shirt for beach wear.
After a few long and sunny Greek island days, (summer: sunrise 5:15am / sunset 9:30pm) you will soon begin to adapt to island ways, usually by the 2nd week in my experience. Separating the artificial from the natural may not always be easy in establishing a Greek island rhythm.