Same sex unions (but not marriages) were legally recognised in Greece in 2015 and attitudes to the LGBT+ community have grown more liberal across the country. However, the Orthodox Church plays a prominent role in shaping society's views on issues such as sexuality, so you may find your sexuality being frowned upon by some locals – especially outside major cities.
Rest assured, Greece is an extremely popular destinations for LGBT+ travellers for a reason. Athens has a busy scene, but most LGBT+ travellers head for the islands. Mykonos has long been famous for its bars, beaches and general hedonism, while Skiathos also has its share of hang-outs. The island of Lesvos (Mytilini), birthplace of the lesbian poet Sappho, has become something of a place of pilgrimage for lesbians.
The Beloved Republic (http://thebelovedrepublic.com) is a company specialising in organising same-sex unions in Greece. For more info on LGBT+ Greece see https://queerintheworld.com/gay-greece.