The best islands to meet young people to party with are: Ios, Mykonos and Santorini but there are places in Crete, Rhodes, Hydra, Paros and Naxos
that can be just as fun and crazy. But the party scene on the islands is seasonal. You can't come in October and expect to have a wild time. The time to come if you want to party is July and especially August when the Greeks and Italians join in. But Athens is a lot of fun in the off-season and there are still bars open on many of the islands.