Even the smallest of the Greek islands have a great number of beaches to satisfy any need and they can be very lively, especially during high seaon.
Kalymnos is well known for cliff clinbing and diving and Paros, Antiparos and Lefkada for wind and kite surfing should any of those may be your thing. Various activities can be found in most of the bigger islands and that does not exclude some of the smaller ones too.
Wild nightlife and partying can be found in Mykonos, while extremeties in that area are in Malia, Laganas, Kavos, Tingaki, mainly.
For a first trip to Greece I'd suggest Corfu ( Kerkira ) , staying in a resort on the north coast like Sidari , Roda or Kassiopi , or go to Crete , staying in Rethymnon province .
best greek island holiday for 2 young 60 year olds. We dont mind the loud music and mix pretty well with any age.
Mykonos
Crete
Skiathos
Rhodes
Ios
This is my own top 5 visit these places and you WON'T regret it ;)
Crete
Cyprus
trust me people those two are the coolest
None go to Cyprus
any of the Cyclades islands
they are the most party oriented